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SAS/ETS 9.2Users Guide

The correct bibliographic citation for this manual is as follows: SAS Institute Inc. 2008. SAS/ETS 9.2 Users Guide. Cary, NC: SAS Institute Inc.

SAS/ETS 9.2 Users GuideCopyright 2008, SAS Institute Inc., Cary, NC, USA ISBN 978-1-59047-949-0 All rights reserved. Produced in the United States of America. For a hard-copy book: No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, or otherwise, without the prior written permission of the publisher, SAS Institute Inc. For a Web download or e-book: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. U.S. Government Restricted Rights Notice: Use, duplication, or disclosure of this software and related documentation by the U.S. government is subject to the Agreement with SAS Institute and the restrictions set forth in FAR 52.227-19, Commercial Computer Software-Restricted Rights (June 1987). SAS Institute Inc., SAS Campus Drive, Cary, North Carolina 27513. 1st electronic book, March 2008 2nd electronic book, February 2009 1st printing, March 2009 SAS Publishing provides a complete selection of books and electronic products to help customers use SAS software to its fullest potential. For more information about our e-books, e-learning products, CDs, and hard-copy books, visit the SAS Publishing Web site at support.sas.com/publishing or call 1-800727-3228. SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS Institute Inc. in the USA and other countries. indicates USA registration. Other brand and product names are registered trademarks or trademarks of their respective companies.

ContentsI General InformationWhats New in SAS/ETS . . . . . . . . . . . . . . . . . . .

13 15 63 129 149 165

Chapter 1. Chapter 2. Chapter 3. Chapter 4. Chapter 5. Chapter 6.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . Working with Time Series Data . . . . . . . . . . . . . . . . . Date Intervals, Formats, and Functions SAS Macros and Functions . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Nonlinear Optimization Methods

II Procedure ReferenceChapter 7. Chapter 8. Chapter 9. The ARIMA Procedure . . . . . . . . . . . . . . . . . . . . The AUTOREG Procedure . . . . . . . . . . . . . . . . . . . The COMPUTAB Procedure . . . . . . . . . . . . . . . . . .

187189 313 429 483 519 615 681 719 773 827 869 943 1261 1349 1375 1441 1511 1541

Chapter 10. The COUNTREG Procedure . . . . . . . . . . . . . . . . . . Chapter 11. The DATASOURCE Procedure . . . . . . . . . . . . . . . . . Chapter 12. The ENTROPY Procedure (Experimental) . . . . . . . . . . . . . Chapter 13. The ESM Procedure . . . . . . . . . . . . . . . . . . . . . Chapter 14. The EXPAND Procedure Chapter 15. The FORECAST Procedure Chapter 16. The LOAN Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . .

Chapter 17. The MDC Procedure . . . . . . . . . . . . . . . . . . . . . Chapter 18. The MODEL Procedure . . . . . . . . . . . . . . . . . . . . Chapter 19. The PANEL Procedure . . . . . . . . . . . . . . . . . . . . Chapter 20. The PDLREG Procedure . . . . . . . . . . . . . . . . . . .

Chapter 21. The QLIM Procedure . . . . . . . . . . . . . . . . . . . . . Chapter 22. The SIMILARITY Procedure (Experimental) . . . . . . . . . . . . Chapter 23. The SIMLIN Procedure . . . . . . . . . . . . . . . . . . . . Chapter 24. The SPECTRA Procedure . . . . . . . . . . . . . . . . . . .

Chapter 25. The STATESPACE Procedure

. . . . . . . . . . . . . . . . .

1567 1613 1679 1727 1741 1855 2033 2101

Chapter 26. The SYSLIN Procedure . . . . . . . . . . . . . . . . . . . . Chapter 27. The TIMESERIES Procedure . . . . . . . . . . . . . . . . . . Chapter 28. The TSCSREG Procedure . . . . . . . . . . . . . . . . . . . Chapter 29. The UCM Procedure . . . . . . . . . . . . . . . . . . . . . Chapter 30. The VARMAX Procedure . . . . . . . . . . . . . . . . . . . Chapter 31. The X11 Procedure Chapter 32. The X12 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

III Data Access EnginesChapter 33. The SASECRSP Interface Engine . . . . . . . . . . . . . . . . Chapter 34. The SASEFAME Interface Engine . . . . . . . . . . . . . . . . Chapter 35. The SASEHAVR Interface Engine . . . . . . . . . . . . . . . .

21872189 2289 2339

IV Time Series Forecasting SystemChapter 36. Overview of the Time Series Forecasting System . . . . . . . . . .

23772379 2383 2439 2453 2491 2511 2545 2553 2661

Chapter 37. Getting Started with Time Series Forecasting . . . . . . . . . . . . Chapter 38. Creating Time ID Variables . . . . . . . . . . . . . . . . . .

Chapter 39. Specifying Forecasting Models . . . . . . . . . . . . . . . . . Chapter 40. Choosing the Best Forecasting Model . . . . . . . . . . . . . . . Chapter 41. Using Predictor Variables . . . . . . . . . . . . . . . . . . . Chapter 42. Command Reference . . . . . . . . . . . . . . . . . . . . . Chapter 43. Window Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 44. Forecasting Process Details

V Investment AnalysisChapter 45. Overview . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 46. Portfolios . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 47. Investments . . . . . . . . . . . . . . . . . . . . . . . .

26952697 2701 2709

iv

Chapter 48. Computations Chapter 49. Analyses

. . . . . . . . . . . . . . . . . . . . . . .

2753 2765 2781

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Chapter 50. Details . . . . . . . . . . . . . . . . . . . . . . . . . .

Subject Index

2793

Syntax Index

2835

v

vi

Credits and Acknowledgments

Credits

DocumentationEditing Technical Review Ed Huddleston, Anne Jones Jackie Allen, Evan L. Anderson, Ming-Chun Chang, Jan Chvosta, Brent Cohen, Allison Crutcheld, Paige Daniels, Gl Ege, Bruce Elsheimer, Donald J. Erdman, Kelly Fellingham, Laura Jackson, Wilma S. Jackson, Wen Ji, Kurt Jones, Kathleen Kiernan, Jennifer Sloan, Michael J. Leonard, Mark R. Little, Kevin Meyer, Gina Marie Mondello, Steve Morrison, Youngjin Park, David Schlotzhauer, Jim Seabolt, Rajesh Selukar, Arthur Sinko, Michele A. Trovero, Charles Sun, Donna E. Woodward

Documentation Production

Michele A. Trovero, Tim Arnold

SoftwareThe procedures in SAS/ETS software were implemented by members of the Advanced Analytics department. Program development includes design, programming, debugging, support, documentation, and technical review. In the following list, the names of the developers who currently support the procedure are listed rst.

ARIMA

Rajesh Selukar, Michael J. Leonard, Terry Woodeld

AUTOREG COMPUTAB COUNTREG DATASOURCE ENTROPY ESM EXPAND FORECAST LOAN MDC MODEL PANEL PDLREG QLIM SIMILARITY SIMLIN SPECTRA STATESPACE SYSLIN TIMESERIES TSCSREG UCM VARMAX X11

Xilong Chen, Arthur Sinko, Jan Chvosta, John P. Sall Michael J. Leonard, Alan R. Eaton, David F. Ross Jan Chvosta, Laura Jackson Kelly Fellingham, Meltem Narter Xilong Chen, Arthur Sinko, Greg Sterijevski, Donald J. Erdman Michael J. Leonard Marc Kessler, Michael J. Leonard, Mark R. Little Michael J. Leonard, Mark R. Little, John P. Sall Gl Ege Jan Chvosta Donald J. Erdman, Mark R. Little, John P. Sall Jan Chvosta, Greg Sterijevski Xilong Chen, Arthur Sinko, Jan Chvosta, Leigh A. Ihnen Jan Chvosta Michael J. Leonard Mark R. Little, John P. Sall Rajesh Selukar, Donald J. Erdman, John P. Sall Donald J. Erdman, Michael J. Leonard Donald J. Erdman, Leigh A. Ihnen, John P. Sall Marc Kessler, Michael J. Leonard Jan Chvosta, Meltem Narter Rajesh Selukar Youngjin Park Wilma S. Jackson, R. Bart Killam, Leigh A. Ihnen,

viii

Richard D. Langston X12 Time Series Investment Analysis System Compiler and Symbolic Differentiation SASEHAVR SASECRSP SASEFAME Testing Wilma S. Jackson Evan L. Anderson, Michael J. Leonard, Meltem Narter, Gl Ege Gl Ege, Scott Gray, Michael J. Leonard

Stacey Christian

Kelly Fellingham Kelly Fellingham, Peng Zang Kelly Fellingham Jackie Allen, Ming-Chun Chang, Bruce Elsheimer, Kelly Fellingham, Jennifer Sloan, Charles Sun, Linda Timberlake, Mark Traccarella, Peng Zang

Technical Support

Members

Paige Daniels, Wen Ji, Kurt Jones, Kathleen Kiernan, Kevin Meyer, Gina Marie Mondello, David Schlotzhauer, Donna E. Woodward

AcknowledgmentsHundreds of people have helped the SAS System in many ways since its inception. The following individuals have been especially helpful in the development of the procedures in SAS/ETS software. Acknowledgments for the SAS System generally appear in Base SAS software documentation and SAS/ETS software documentation.

ix

David Amick David M. DeLong David Dickey Douglas J. Drummond William Fortney Wayne Fuller A. Ronald Gallant Phil Hanser Marvin Jochimsen Jeff Kaplan Ken Kraus George McCollister Douglas Miller Brian Monsell Robert Parks Gregory Sali Bob Spatz Mary Young

Idaho Ofce of Highway Safety Duke University North Carolina State University Center for Survey Statistics Boeing Computer Services Iowa State University The University North Carolina at Chapel Hill Sacramento Municipal Utilities District Mississippi R&O Center Sun Guard Center for Research in Security Prices San Diego Gas & Electric Purdue University U.S. Census Bureau Washington University Idaho Ofce of Highway Safety Center for Research in Security Prices Salt River Project

The nal responsibility for the SAS System lies with SAS Institute alone. We hope that you will always let us know your opinions about the SAS System and its documentation. It is through your participation that SAS software is continuously improved.

x

Part I

General Information

2

Chapter 1

Whats New in SAS/ETSContentsWhats New in SAS/ETS for SAS 9.2 . . . . . . . . Overview . . . . . . . . . . . . . . . . . . . . AUTOREG Procedure . . . . . . . . . . . . . COUNTREG Procedure . . . . . . . . . . . . DATASOURCE Procedure . . . . . . . . . . . New ESM Procedure . . . . . . . . . . . . . . MODEL Procedure . . . . . . . . . . . . . . PANEL Procedure . . . . . . . . . . . . . . . QLIM Procedure . . . . . . . . . . . . . . . . SASECRSP Engine . . . . . . . . . . . . . . SASEFAME Engine . . . . . . . . . . . . . . SASEHAVR Engine . . . . . . . . . . . . . . New SIMILARITY Procedure (Experimental) UCM Procedure . . . . . . . . . . . . . . . . VARMAX Procedure . . . . . . . . . . . . . X12 Procedure . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 3 4 5 5 5 5 6 6 7 7 8 9 9 10 12 13

This chapter summarizes the new features available in SAS/ETS software with SAS 9.2. It also describes other new features that were added with SAS 9.1.

Whats New in SAS/ETS for SAS 9.2

OverviewMany SAS/ETS procedures now produce graphical output using the SAS Output Delivery System. This output is produced when you turn on ODS graphics with the following ODS statement:ods graphics on;

4 ! Chapter 1: Whats New in SAS/ETS

Several procedures now support the PLOTS= option to control the graphical output produced. (See the chapters for individual SAS/ETS procedures for details on the plots supported.) With SAS 9.2, SAS/ETS offers three new modules: The new ESM procedure provides forecasting using exponential smoothing models with optimized smoothing weights. The SASEHAVR interface engine is now production and available to Windows users for accessing economic and nancial data residing in a HAVER ANALYTICS Data Link Express (DLX) database. The new SIMILARITY (experimental) procedure provides similarity analysis of time series data. New features have been added to the following SAS/ETS components: PROC AUTOREG PROC COUNTREG PROC DATASOURCE PROC MODEL PROC PANEL PROC QLIM SASECRSP Interface Engine SASEFAME Interface Engine SASEHAVR Interface Engine PROC UCM PROC VARMAX PROC X12

AUTOREG ProcedureTwo new features have been added to the AUTOREG procedure. An alternative test for stationarity, proposed by Kwiatkowski, Phillips, Schmidt, and Shin (KPSS), is implemented. The null hypothesis for this test is a stationary time series, which is a natural choice for many applications. Bartlett and quadratic spectral kernels for estimating long-run variance can be used. Automatic bandwidth selection is an option.

COUNTREG Procedure ! 5

Corrected Akaike information criterion (AICC) is implemented. This modication of AIC corrects for small-sample bias. Along with the corrected Akaike information criterion, the mean absolute error (MAE) and mean absolute percentage error (MAPE) are now included in the summary statistics.

COUNTREG ProcedureOften the data that is being analyzed take the form of nonnegative integer (count) values. The new COUNTREG procedure implements count data models that take this discrete nature of data into consideration. The dependent variable in these models is a count that represents various discrete events (such as number of accidents, number of doctor visits, or number of children). The conditional mean of the dependent variable is a function of various covariates. Typically, you are interested in estimating the probability of the number of event occurrences using maximum likelihood estimation. The COUNTREG procedure supports the following types of models: Poisson regression negative binomial regression with linear (NEGBIN1) and quadratic (NEGBIN2) variance functions (Cameron and Trivedi 1986) zero-inated Poisson (ZIP) model (Lambert 1992) zero-inated negative binomial (ZINB) model

DATASOURCE ProcedurePROC DATASOURCE now supports the newest Compustat Industrial Universal Character Annual and Quarterly data by providing the new letypes CSAUCY3 for annual data and CSQUCY3 for quarterly data.

New ESM ProcedureThe ESM (Exponential Smoothing Models) procedure provides a quick way to generate forecasts for many time series or transactional data in one step. All parameters associated with the forecast model are optimized based on the data.

MODEL ProcedureThe t copula and the normal mixture copula have been added to the MODEL procedure. Both copulas support asymmetric parameters. The copula is used to modify the correlation structure of


the model residuals for simulation. Starting with SAS 9.2, the MODEL procedure stores MODEL les in SAS datasets using an XMLlike format instead of in SAS catalogs. This makes MODEL les more readily extendable in the future and enables Java-based applications to read the MODEL les directly. More information is stored in the new format MODEL les; this enables some features that are not available when the catalog format is used. The MODEL procedure continues to read and write old-style catalog MODEL les, and model les created by previous releases of SAS/ETS continue to work, so you should experience no direct impact from this change. The CMPMODEL= option can be used in an OPTIONS statement to modify the behavior of the MODEL when reading and writing MODEL les. The values allowed are CMPMODEL= BOTH | XML | CATALOG. For example, the following statements restore the previous behavior:options cmpmodel=catalog;

The CMPMODEL= option defaults to BOTH in SAS 9.2; this option is intended for transitional use while customers become accustomed to the new le format. If CMPMODEL=BOTH, the MODEL procedure writes both formats; when loading model les, PROC MODEL attempts to load the XML version rst and the CATALOG version second (if the XML version is not found). If CMPMODEL=XML the MODEL procedure reads and writes only the XML format. If CMPMODEL=CATALOG, only the catalog format is used.

PANEL ProcedureThe PANEL procedure expands the estimation capability of the TSCSREG procedure in the timeseries cross-sectional framework. The new methods include: between estimators, pooled estimators, and dynamic panel estimators using GMM method. Creating lags of variables in a panel setting is simplied by the LAG statement. Because the presence of heteroscedasticity can result in inefcient and biased estimates of the variance covariance matrix in the OLS framework, several methods that produce heteroscedasticity-corrected covariance matrices (HCCME) are added. The new RESTRICT statement species linear restrictions on the parameters. New ODS Graphics plots simplify model development by providing visual analytical tools.

QLIM ProcedureStochastic frontier models are now available in the QLIM procedure. Specication of these models allows for random shocks of production or cost along with technological or cost inefciencies. The nonnegative error-term component that represents technological or cost inefciencies has halfnormal, exponential, or truncated normal distributions.

SASECRSP Engine ! 7

SASECRSP EngineThe SASECRSP interface now supports reading of CRSP stock, indices, and combined stock/indices databases by using a variety of keys, not just CRSPs primary key PERMNO. In addition, SASECRSP can now read the CRSP/Compustat Merged (CCM) database and fully supports cross-database access, enabling you to access the CCM database by CRSPs main identiers PERMNO and PERMCO, as well as to access the CRSP Stock databases by Compustats GVKEY identier. A list of other new features follows: SASECRSP now fully supports access of scal CCM data members by both scal and calendar date range restrictions. Fiscal to calendar date shifting has been added as well. New date elds have been added for CCM scal members. Now scal members have three different dates: a CRSP date, a scal integer date, and a calendar integer date. An additional date function has been added which enables you to convert from scal to calendar dates. Date range restriction for segment members has also been added.

SASEFAME EngineThe SASEFAME interface enables you to access and process nancial and economic time series data that resides in a FAME database. SASEFAME for SAS 9.2 supports Windows, Solaris, AIX, Linux, Linux Opteron, and HP-UX hosts. You can now use the SAS windowing environment to view FAME data and use the SAS viewtable commands to navigate your FAME data base. You can select the time span of data by specifying a range of dates in the RANGE= option. You can use an input SAS data set with a WHERE clause to specify selection of variables based on BY variables, such as tickers or issues stored in a FAME string case series. You can use a FAME crosslist to perform selection based on the crossproduct of two FAME namelists. The new FAMEOUT= option now supports the following classes and types of data series objects: FORMULA, TIME, BOOLEAN, CASE, DATE, and STRING. It is easy to use a SAS input data set with the INSET= option to create a specic view of your FAME data. Multiple views can be created by using multiple LIBNAME statements with customized options tailored to the unique view that you want to create. See Example 34.10: Selecting Time Series Using CROSSLIST= Option with INSET= and WHERE=TICK on page 2325 in Chapter 34, The SASEFAME Interface Engine. The INSET variables dene the BY variables that enable you to view cross sections or slices of your data. When used in conjunction with the WHERE clause and the CROSSLIST= option, SASEFAME can show any or all of your BY groups in the same view or in multiple views. The INSET= option is invalid without a WHERE that clause species the BY variables you want to use in your view, and it must be used with the CROSSLIST=option.


The CROSSLIST= option provides a more efcient means of selecting cross sections of nancial time series data. This option can be used without using the INSET= option. There are two methods for performing the crosslist selection function. The rst method uses two FAME namelists, and the second method uses one namelist and one BY group specied in the WHERE= clause of the INSET=option. See Example 34.9: Selecting Time Series Using CROSSLIST= Option with a FAME Namelist of Tickers on page 2322 in Chapter 34, The SASEFAME Interface Engine. The FAMEOUT= option provides efcient selection of the class and type of the FAME data series objects you want in your SAS output data set. The possible values for fame_data_object_class_type are FORMULA, TIME, BOOLEAN, CASE, DATE, and STRING. If the FAMEOUT=option is not specied, numeric time series are output to the SAS data set. FAMEOUT=CASE defaults to case series of numeric type, so if you want another type of case series in your output, then you must specify it. Scalar data objects are not supported. See Example 34.6: Reading Other FAME Data Objects with the FAMEOUT= Option on page 2316 in Chapter 34, The SASEFAME Interface Engine.

SASEHAVR EngineThe SASEHAVR interface engine is now production, giving Windows users random access to economic and nancial data that resides in a Haver Analytics Data Link Express (DLX) database. You can now use the SAS windowing environment to view HAVERDLX data and use the SAS viewtable commands to navigate your Haver database. You can use the SQL procedure to create a view of your resulting SAS data set. You can limit the range of data that is read from the time series and specify a desired conversion frequency. Start dates are recommended in the LIBNAME statement to help you save resources when processing large databases or when processing a large number of observations. You can further subset your data by using the WHERE, KEEP, or DROP statements in your DATA step. New options are provided for more efcient subsetting by time series variables, groups, or sources. You can force the aggregation of all variables selected to be of the frequency specied by the FREQ= option if you also specify the FORCE=FREQ option. Aggregation is supported only from a more frequent time interval to a less frequent time interval, such as from weekly to monthly. A list of other new features follows: You can see the available data sets in the SAS LIBNAME window of the SAS windowing environment by selecting the SASEHAVR libref in the LIBNAME window that you have previously used in your LIBNAME statement. You can view your SAS output observations by double clicking on the desired output data set libref in the libname window of the SAS windowing environment. You can type Viewtable on the SAS command line to view any of your SASEHAVR tables, views, or librefs, both for input and output data sets. By default, the SASEHAVR engine reads all time series in the Haver database that you reference by using your SASEHAVR libref. The START= option is specied in the form YYYYMMDD, as is the END= option. The start and end dates are used to limit the time span of data; they can help you save resources when processing large databases or when processing a large number of observations.

New SIMILARITY Procedure (Experimental) ! 9

It is also possible to select specic variables to be included or excluded from the SAS data set by using the KEEP= or the DROP= option. When the KEEP= or the DROP= option is used, the resulting SAS data set keeps or drops the variables that you select in that option. There are three wildcards currently available: *, ?, and #. The * wildcard corresponds to any character string and will include any string pattern that corresponds to that position in the matching variable name. The ? means that any single alphanumeric character is valid. The # wildcard corresponds to a single numeric character. You can also select time series in your data by using the GROUP= or the SOURCE= option to select on group name or on source name. Alternatively, you can deselect time series by using the DROPGROUP= or the DROPSOURCE= option. These options also support the wildcards *, ?, and #. By default, SASEHAVR selects only the variables that are of the specied frequency in the FREQ= option. If this option is not specied, SASEHAVR selects the variables that match the frequency of the rst selected variable. If no other selection criteria are specied, the rst selected variable is the rst physical DLXRecord read from the Haver database. The FORCE=FREQ option can be specied to force the aggregation of all variables selected to be of the frequency specied by the FREQ= option. Aggregation is supported only from a more frequent time interval to a less frequent time interval, such as from weekly to monthly. The FORCE= option is ignored if the FREQ= option is not specied.

New SIMILARITY Procedure (Experimental)The new SIMILARITY procedure provides similarity analysis between two time series and other sequentially ordered numeric data. The SIMILARITY procedure computes similarity measures between an input sequence and target sequence, as well as similarity measures that slide the target sequence with respect to the input sequence. The slides can be by observation index (sliding-sequence similarity measures) or by seasonal index (seasonal-sliding-sequence similarity measures).

UCM ProcedureThe following features are new to the UCM procedure: The new RANDOMREG statement enables specication of regressors with time-varying regression coefcients. The coefcients are assumed to follow independent random walks. Multiple RANDOMREG statements can be specied, and each statement can specify multiple regressors. The regression coefcient random walks for regressors specied in the same RANDOMREG statement are assumed to have the same disturbance variance parameter. This arrangement enables a very exible specication of regressors with time-varying coefcients.


The new SPLINEREG statement enables specication of a spline regressor that can optionally have time-varying coefcients. The spline specication is useful when the series being forecast depends on a regressor in a nonlinear fashion. The new SPLINESEASON statement enables parsimonious modeling of long and complex seasonal patterns using the spline approximation. The SEASON statement now has options that enable complete control over the constituent harmonics that make up the trigonometric seasonal model. It is now easy to obtain diagnostic test statistics useful for detecting structural breaks such as additive outliers and level shifts. As an experimental feature, you can now model the irregular component as an autoregressive moving-average (ARMA) process. The memory management and numerical efciency of the underlying algorithms have been improved.

VARMAX ProcedureThe VARMAX procedure now enables independent (exogenous) variables with their distributed lags to inuence dependent (endogenous) variables in various models, such as VARMAX, BVARX, VECMX, BVECMX, and GARCH-type multivariate conditional heteroscedasticity models.

Multivariate GARCH ModelsNew GARCH StatementMultivariate GARCH modeling is now a production feature of VARMAX. To enable greater exibility in specifying multivariate GARCH models, the new GARCH statement has been added to the VARMAX procedure. With the addition of the GARCH statement, the GARCH= option is no longer supported on the MODEL statement. The OUTHT= option can be specied in the GARCH statement to write the estimated conditional covariance matrix to an output data set. See GARCH Statement on page 1907 in Chapter 30, The VARMAX Procedure, for details.

The VARMAX ModelThe VARMAX procedure provides modeling of a VARMAX(p; q; s) process which is written asp X i D1 s X i D0 q X i D1 i,

yt D C

i yt

i

C

i xt

i

C

t

i

t i

where .B/ D Ik Pq i iD1 i B .

Pp

i D1 i B

.B/ D 0 C 1 B C

C s B s , and .B/ D Ik

VARMAX Procedure ! 11

If the Kalman ltering method is used for the parameter estimation of the VARMAX(p,q,s) model, then the dimension of the state-space vector is large, which takes time and memory for computing. For convenience, the parameter estimation of the VARMAX(p,q,s) model uses the two-stage estimation method, which computes the estimation of deterministic terms and exogenous parameters and then maximizes the log-likelihood function of the VARMA(p,q) model. Some examples of VARMAX modeling are:model y1 y2 = x1 / q=1; nloptions tech=qn; model y1 y2 = x1 / p=1 q=1 xlag=1 nocurrentx; nloptions tech=qn;

The BVARX ModelBayesian modeling allows independent (exogenous) variables with their distributed lags. For example:model y1 y2 = x1 / p=2 prior=(theta=0.2 lambda=5);

The VECMX ModelVector error correction modeling now allows independent (exogenous) variables with their distributed lags. For example:model y1 y2 = x1 / p=2 ecm=(rank=1);

The BVECMX ModelBayesian vector error correction modeling allows independent (exogenous) variables with their distributed lags. For example:model y1 y2 = x1 / p=2 prior=(theta=0.2 lambda=5) ecm=(rank=1);

The VARMAX-GARCH ModelVARMAX modeling now supports an error term that has a GARCH-type multivariate conditional heteroscedasticity model. For example:model y1 y2 = x1 / p=1 q=1; garch q=1;


New Printing Control OptionsThe PRINT= option can be used in the MODEL statement to control the results printed. See the description of the PRINT= option in Chapter 30, The VARMAX Procedure, for details.

X12 ProcedureThe X12 procedure has many new statements and options. Many of the new features are related to the regARIMA modeling, which is used to extend the series to be seasonally adjusted. A new experimental input and output data set has been added which describes the times series model t to the series. The following miscellaneous statements and options are new: The NOINT option on the AUTOMDL statement suppresses the tting of a constant term in automatically identied models. The following tables are now available through the OUTPUT statement: A7, A9, A10, C20, D1, and D7. The TABLES statement enables you to display some tables that represent intermediate calculations in the X11 method and that are not displayed by default. The following statements and options related to the regression component of regARIMA modeling are new: The SPAN= option on the OUTLIER statement can be used to limit automatic outlier detection to a subset of the time series observations. The following predened variables have been added to the PREDEFINED option on the REGRESSION statement: EASTER(value), SCEASTER(value), LABOR(value), THANK(value), TDSTOCK(value), SINCOS(value . . . ). User-dened regression variables can be included on the regression model by specifying them in the USERVAR=(variables) option in the REGRESSION statement or the INPUT statement. Events can be included as user-dened regression variables in the regression model by specifying them in the EVENT statement. SAS predened events do not require an INEVENT= data set, but an INEVENT= data set can be specied to dene other events. You can now supply initial or xed parameter values for regression variables by using the B=(value < F > . . . ) option in the EVENT statement, the B=(value < F > . . . ) option in the INPUT statement, the B=(value < F > . . . ) option in the REGRESSION statement, or by using the MDLINFOIN= data set in the PROC X12 statement. Some regression variable parameters can be xed while others are estimated.

References ! 13

You can now assign user-dened regression variables to a group by the USERTYPE= option in the EVENT statement, the USERTYPE= option in the INPUT statement, the USERTYPE= option in the REGRESSION statement, or by using the MDLINFOIN= data set in the PROC X12 statement. Census Bureau predened variables are automatically assigned to a regression group, and this cannot be modied. But assigning user-dened regression variables to a regression group allows them to be processed similarly to the predened variables. You can now supply initial or xed parameters for ARMA coefcients using the MDLINFOIN= data set in the PROC X12 statement. Some ARMA coefcients can be xed while others are estimated. The INEVENT= option on the PROC X12 statement enables you to supply an EVENT definition data set so that the events dened in the EVENT denition data set can be used as user-dened regressors in the regARIMA model. User-dened regression variables in the input data set can be identied by specifying them in the USERDEFINED statement. User-dened regression variables specied in the USERVAR=(variables) option of the REGRESSION statement or the INPUT statement do not need to be specied in the USERDEFINED statement, but user-dened variables specied only in the MDLINFOIN= data set need to be idented in the USERDEFINED statement. The following new experimental options specify input and output data sets that describe the times series model: The MDLINFOIN= and MDLINFOOUT= data sets specied in the PROC X12 statement enable you to store the results of model identication and use the stored information as input when executing the X12 Procedure.

ReferencesCenter for Research in Security Prices (2003), CRSP/Compustat Merged Database Guide, Chicago: The University of Chicago Graduate School of Business, http://www.crsp.uchicago.edu/ support/documentation/pdfs/ccm_database_guide.pdf. Center for Research in Security Prices (2003), CRSP Data Description Guide, Chicago: The University of Chicago Graduate School of Business, http://www.crsp.uchicago.edu/ support/documentation/pdfs/stock_indices_data_descriptions.pdf. Center for Research in Security Prices (2002), CRSP Programmers Guide, Chicago: The University of Chicago Graduate School of Business, http://www.crsp.uchicago.edu/support/ documentation/pdfs/stock_indices_programming.pdf. Center for Research in Security Prices (2003), CRSPAccess Database Format Release Notes, Chicago: The University of Chicago Graduate School of Business, http://www.crsp. uchicago.edu/support/documentation/release_notes.html.


Center for Research in Security Prices (2003), CRSP Utilities Guide, Chicago: The University of Chicago Graduate School of Business, http://www.crsp.uchicago.edu/support/ documentation/pdfs/stock_indices_utilities.pdf. Center for Research in Security Prices (2002), CRSP SFA Guide, Chicago: The University of Chicago Graduate School of Business. Gomez, V. and Maravall, A. (1997a), Program TRAMO and SEATS: Instructions for the User, Beta Version, Banco de Espana. Gomez, V. and Maravall, A. (1997b), Guide for Using the Programs TRAMO and SEATS, Beta Version, Banco de Espana. Haver Analytics (2001), DLX API Programmers Reference, New York, NY. Stoffer, D. and Toloi, C. (1992), A Note on the Ljung-Box-Pierce Portmanteau Statistic with Missing Data, Statistics & Probability Letters 13, 391-396. SunGard Data Management Solutions (1998), Guide to FAME Database Servers, 888 Seventh Avenue, 12th Floor, New York, NY 10106 USA, http://www.fame.sungard.com/support. html, http://www.data.sungard.com. SunGard Data Management Solutions (1995), Users Guide to FAME, Ann Arbor, MI, http:// www.fame.sungard.com/support.html. SunGard Data Management Solutions (1995), Reference Guide to Seamless C HLI, Ann Arbor, MI, http://www.fame.sungard.com/support.html. SunGard Data Management Solutions(1995), Command Reference for Release 7.6, Vols. 1 and 2, Ann Arbor, MI, http://www.fame.sungard.com/support.html.

Chapter 2

IntroductionContentsOverview of SAS/ETS Software . . . . . . . . . . . . . . . . . . . . . . . . . . . Uses of SAS/ETS Software . . . . . . . . . . . . . . . . . . . . . . . . . . Contents of SAS/ETS Software . . . . . . . . . . . . . . . . . . . . . . . . Experimental Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . About This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typographical Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . Where to Turn for More Information . . . . . . . . . . . . . . . . . . . . . . . . . Accessing the SAS/ETS Sample Library . . . . . . . . . . . . . . . . . . . Online Help System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SAS Short Courses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SAS Technical Support Services . . . . . . . . . . . . . . . . . . . . . . . . Major Features of SAS/ETS Software . . . . . . . . . . . . . . . . . . . . . . . . Discrete Choice and Qualitative and Limited Dependent Variable Analysis . Regression with Autocorrelated and Heteroscedastic Errors . . . . . . . . . Simultaneous Systems Linear Regression . . . . . . . . . . . . . . . . . . . Linear Systems Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . Polynomial Distributed Lag Regression . . . . . . . . . . . . . . . . . . . . Nonlinear Systems Regression and Simulation . . . . . . . . . . . . . . . . ARIMA (Box-Jenkins) and ARIMAX (Box-Tiao) Modeling and Forecasting Vector Time Series Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . State Space Modeling and Forecasting . . . . . . . . . . . . . . . . . . . . Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Seasonal Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Structural Time Series Modeling and Forecasting . . . . . . . . . . . . . . . Time Series Cross-Sectional Regression Analysis . . . . . . . . . . . . . . . Automatic Time Series Forecasting . . . . . . . . . . . . . . . . . . . . . . Time Series Interpolation and Frequency Conversion . . . . . . . . . . . . . Trend and Seasonal Analysis on Transaction Databases . . . . . . . . . . . Access to Financial and Economic Databases . . . . . . . . . . . . . . . . . Spreadsheet Calculations and Financial Report Generation . . . . . . . . . . Loan Analysis, Comparison, and Amortization . . . . . . . . . . . . . . . . Time Series Forecasting System . . . . . . . . . . . . . . . . . . . . . . . . Investment Analysis System . . . . . . . . . . . . . . . . . . . . . . . . . . 16 17 18 20 20 21 22 22 22 23 23 23 23 24 26 27 28 29 29 31 32 33 34 35 36 37 37 39 41 42 44 44 45 46

16 ! Chapter 2: Introduction

ODS Graphics . . . . . . . . . . . . . . . . Related SAS Software . . . . . . . . . . . . . . . Base SAS Software . . . . . . . . . . . . . SAS Forecast Studio . . . . . . . . . . . . . SAS High-Performance Forecasting . . . . . SAS/GRAPH Software . . . . . . . . . . . SAS/STAT Software . . . . . . . . . . . . . SAS/IML Software . . . . . . . . . . . . . . SAS Stat Studio . . . . . . . . . . . . . . . SAS/OR Software . . . . . . . . . . . . . . SAS/QC Software . . . . . . . . . . . . . . MLE for User-Dened Likelihood Functions JMP Software . . . . . . . . . . . . . . . . SAS Enterprise Guide . . . . . . . . . . . . SAS Add-In for Microsoft Ofce . . . . . . Enterprise MinerTime Series nodes . . . . SAS Risk Products . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . .

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Overview of SAS/ETS SoftwareSAS/ETS software, a component of the SAS System, provides SAS procedures for: econometric analysis time series analysis time series forecasting systems modeling and simulation discrete choice analysis analysis of qualitative and limited dependent variable models seasonal adjustment of time series data nancial analysis and reporting access to economic and nancial databases time series data management In addition to SAS procedures, SAS/ETS software also includes seamless access to economic and nancial databases and interactive environments for time series forecasting and investment analysis.

Uses of SAS/ETS Software ! 17

Uses of SAS/ETS SoftwareSAS/ETS software provides tools for a wide variety of applications in business, government, and academia. Major uses of SAS/ETS procedures are economic analysis, forecasting, economic and nancial modeling, time series analysis, nancial reporting, and manipulation of time series data. The common theme relating the many applications of the software is time series data: SAS/ETS software is useful whenever it is necessary to analyze or predict processes that take place over time or to analyze models that involve simultaneous relationships. Although SAS/ETS software is most closely associated with business, nance and economics, time series data also arise in many other elds. SAS/ETS software is useful whenever time dependencies, simultaneous relationships, or dynamic processes complicate data analysis. For example, an environmental quality study might use SAS/ETS softwares time series analysis tools to analyze pollution emissions data. A pharmacokinetic study might use SAS/ETS softwares features for nonlinear systems to model the dynamics of drug metabolism in different tissues. The diversity of problems for which econometrics and time series analysis tools are needed is reected in the applications reported by SAS users. The following listed items are some applications of SAS/ETS software presented by SAS users at past annual conferences of the SAS Users Group International (SUGI). forecasting college enrollment (Calise and Earley 1997) tting a pharmacokinetic model (Morelock et al. 1995) testing interaction effect in reducing sudden infant death syndrome (Fleming, Gibson, and Fleming 1996) forecasting operational indices to measure productivity changes (McCarty 1994) spectral decomposition and reconstruction of nuclear plant signals (Hoyer and Gross 1993) estimating parameters for the constant-elasticity-of-substitution translog model (Hisnanick 1993) applying econometric analysis for mass appraisal of real property (Amal and Weselowski 1993) forecasting telephone usage data (Fishetti, Heathcote, and Perry 1993) forecasting demand and utilization of inpatient hospital services (Hisnanick 1992) using conditional demand estimation to determine electricity demand (Keshani and Taylor 1992) estimating tree biomass for measurement of forestry yields (Parresol and Thomas 1991) evaluating the theory of input separability in the production function of U.S. manufacturing (Hisnanick 1991)


forecasting dairy milk yields and composition (Benseman 1990) predicting the gloss of coated aluminum products subject to weathering (Khan 1990) learning curve analysis for predicting manufacturing costs of aircraft (Le Bouton 1989) analyzing Dow Jones stock index trends (Early, Sweeney, and Zekavat 1989) analyzing the usefulness of the composite index of leading economic indicators for forecasting the economy (Lin and Myers 1988)

Contents of SAS/ETS SoftwareProceduresSAS/ETS software includes the following SAS procedures: ARIMA AUTOREG COMPUTAB COUNTREG DATASOURCE ENTROPY ESM EXPAND FORECAST LOAN MDC MODEL PANEL PDLREG QLIM SIMILARITY SIMLIN SPECTRA STATESPACE SYSLIN ARIMA (Box-Jenkins) and ARIMAX (Box-Tiao) modeling and forecasting regression analysis with autocorrelated or heteroscedastic errors and ARCH and GARCH modeling spreadsheet calculations and nancial report generation regression modeling for dependent variables that represent counts access to nancial and economic databases maximum entropy-based regression forecasting by using exponential smoothing models with optimized smoothing weights time series interpolation, frequency conversion, and transformation of time series automatic forecasting loan analysis and comparison multinomial discrete choice analysis nonlinear simultaneous equations regression and nonlinear systems modeling and simulation panel data models polynomial distributed lag regression qualitative and limited dependent variable analysis similarity analysis of time series data for time series data mining linear systems simulation spectral and cross-spectral analysis state space modeling and automated forecasting of multivariate time series linear simultaneous equations models

Contents of SAS/ETS Software ! 19

TIMESERIES TSCSREG UCM VARMAX X11 X12

analysis of time-stamped transactional data time series cross-sectional regression analysis unobserved components analysis of time series vector autoregressive and moving-average modeling and forecasting seasonal adjustment (Census X-11 and X-11 ARIMA) seasonal adjustment (Census X-12 ARIMA)

MacrosSAS/ETS software includes the following SAS macros: %AR %BOXCOXAR %DFPVALUE %DFTEST %LOGTEST %MA %PDL generates statements to dene autoregressive error models for the MODEL procedure investigates Box-Cox transformations useful for modeling and forecasting a time series computes probabilities for Dickey-Fuller test statistics performs Dickey-Fuller tests for unit roots in a time series process tests to determine whether a log transformation is appropriate for modeling and forecasting a time series generates statements to dene moving-average error models for the MODEL procedure generates statements to dene polynomial distributed lag models for the MODEL procedure

These macros are part of the SAS AUTOCALL facility and are automatically available for use in your SAS program. Refer to SAS Macro Language: Reference for information about the SAS macro facility.

Access Interfaces to Economic and Financial DatabasesIn addition to PROC DATASOURCE, these SAS/ETS access interfaces provide seamless access to nancial and economic databases: SASECRSP SASEFAME SASEHAVR LIBNAME engine for accessing time series and event data residing in CRSPAccess database. LIBNAME engine for accessing time or case series data residing in a FAME database. LIBNAME engine for accessing time series residing in a HAVER ANALYTICS Data Link Express (DLX) database.


The Time Series Forecasting SystemSAS/ETS software includes an interactive forecasting system, described in Part IV. This graphical user interface to SAS/ETS forecasting features was developed with SAS/AF software and uses PROC ARIMA and other internal routines to perform time series forecasting. The Time Series Forecasting System makes it easy to forecast time series and provides many features for graphical data exploration and graphical comparisons of forecasting models and forecasts. (You must have SAS/GRAPH installed to use the graphical features of the system.)

The Investment Analysis SystemThe Investment Analysis System, described in Part V, is an interactive environment for analyzing the time-value of money in a variety of investments. Various analyses are provided to help analyze the value of investment alternatives: time value, periodic equivalent, internal rate of return, benetcost ratio, and break-even analysis.

Experimental SoftwareExperimental software is sometimes included as part of a production-release product. It is provided to (sometimes targeted) customers in order to obtain feedback. All experimental uses are marked Experimental in this document. Whenever an experimental procedure, statement, or option is used, a message is printed to the SAS log to indicate that it is experimental. The design and syntax of experimental software might change before any production release. Experimental software has been tested prior to release, but it has not necessarily been tested to productionquality standards, and so should be used with care.

About This BookThis book is a users guide to SAS/ETS software. Since SAS/ETS software is a part of the SAS System, this book assumes that you are familiar with Base SAS software and have the books SAS Language Reference: Dictionary and Base SAS Procedures Guide available for reference. It also assumes that you are familiar with SAS data sets, the SAS DATA step, and with basic SAS procedures such as PROC PRINT and PROC SORT. Chapter 3, Working with Time Series Data, in this book summarizes the aspects of Base SAS software that are most relevant to the use of SAS/ETS software.

Chapter Organization ! 21

Chapter OrganizationFollowing a brief Whats New, this book is divided into ve major parts. Part I contains general information to aid you in working with SAS/ETS Software. Part II explains the SAS procedures of SAS/ETS software. Part III describes the available data access interfaces for economic and nancial databases. Part IV is the reference for the Time Series Forecasting System, an interactive forecasting menu system that uses PROC ARIMA and other routines to perform time series forecasting. Finally, Part V is the reference for the Investment Analysis System. The new features added to SAS/ETS software since the publication of SAS/ETS Software: Changes and Enhancements for Release 8.2 are summarized in Chapter 1, Whats New in SAS/ETS. If you have used SAS/ETS software in the past, you may want to skim this chapter to see whats new. Part I contains the following chapters. Chapter 2, the current chapter, provides an overview of SAS/ETS software and summarizes related SAS publications, products, and services. Chapter 3, Working with Time Series Data, discusses the use of SAS data management and programming features for time series data. Chapter 4, Date Intervals, Formats, and Functions, summarizes the time intervals, date and datetime informats, date and datetime formats, and date and datetime functions available in the SAS System. Chapter 5, SAS Macros and Functions, documents SAS macros and DATA step nancial functions provided with SAS/ETS software. The macros use SAS/ETS procedures to perform Dickey-Fuller tests, test for the need for log transformations, or select optimal Box-Cox transformation parameters for time series data. Chapter 6, Nonlinear Optimization Methods, documents the NonLinear Optimization subsystem used by some ETS procedures to perform nonlinear optimization tasks. Part II contains chapters that explain the SAS procedures that make up SAS/ETS software. These chapters appear in alphabetical order by procedure name. Part III contains chapters that document the ETS access interfaces to economic and nancial databases. Each of the chapters that document the SAS/ETS procedures (Part II) and the SAS/ETS access interfaces (Part III) is organized as follows: 1. The Overview section gives a brief description of the procedure. 2. The Getting Started section provides a tutorial introduction on how to use the procedure. 3. The Syntax section is a reference to the SAS statements and options that control the procedure. 4. The Details section discusses various technical details. 5. The Examples section contains examples of the use of the procedure.


6. The References section contains technical references on methodology. Part IV contains the chapters that document the features of the Time Series Forecasting System. Part V contains chapters that document the features of the Investment Analysis System.

Typographical ConventionsThis book uses several type styles for presenting information. The following list explains the meaning of the typographical conventions used in this book: roman UPPERCASE ROMAN is the standard type style used for most text. is used for SAS statements, options, and other SAS language elements when they appear in the text. However, you can enter these elements in your own SAS programs in lowercase, uppercase, or a mixture of the two. is used in the Syntax sections initial lists of SAS statements and options. is used for user-supplied values for options in the syntax denitions. In the text, these values are written in italic. is used for the names of variables and data sets when they appear in the text. is used to refer to matrices and vectors and to refer to commands. is used for terms that are dened in the text, for emphasis, and for references to publications. is used for example code. In most cases, this book uses lowercase type for SAS statements.

UPPERCASE BOLDobliquehelvetica

bold italicbold monospace

Where to Turn for More InformationThis section describes other sources of information about SAS/ETS software.

Accessing the SAS/ETS Sample LibraryThe SAS/ETS Sample Library includes many examples that illustrate the use of SAS/ETS software, including the examples used in this documentation. To access these sample programs, select Help from the menu and then select SAS Help and Documentation. From the Contents list, select the section Sample SAS Programs under Learning to Use SAS.

Online Help System ! 23

Online Help SystemYou can access online help information about SAS/ETS software in two ways, depending on whether you are using the SAS windowing environment in the command line mode or the pulldown menu mode. If you are using a command line, you can access the SAS/ETS help menus by typing help on the SAS windowing environment command line. Or you can issue the command help ARIMA (or another procedure name) to display the help for that particular procedure. If you are using the SAS windowing environment pull-down menus, you can pull-down the Help menu and make the following selections: SAS Help and Documentation Learning to Use SAS in the Contents list SAS Products SAS/ETS The content of the Online Help System follows closely that of this book.

SAS Short CoursesThe SAS Education Division offers a number of training courses that might be of interest to SAS/ETS users. Please check the SAS web site for the current list of available training courses.

SAS Technical Support ServicesAs with all SAS products, the SAS Technical Support staff is available to respond to problems and answer technical questions regarding the use of SAS/ETS software.

Major Features of SAS/ETS SoftwareThe following sections briey summarize major features of SAS/ETS software. See the chapters on individual procedures for more detailed information.


Discrete Choice and Qualitative and Limited Dependent Variable AnalysisThe MDC procedure provides maximum likelihood (ML) or simulated maximum likelihood estimates of multinomial discrete choice models in which the choice set consists of unordered multiple alternatives. The MDC procedure supports the following models and features: conditional logit nested logit heteroscedastic extreme value multinomial probit mixed logit pseudo-random or quasi-random numbers for simulated maximum likelihood estimation bounds imposed on the parameter estimates linear restrictions imposed on the parameter estimates SAS data set containing predicted probabilities and linear predictor (x0 ) values decision tree and nested logit model t and goodness-of-t measures including likelihood ratio Aldrich-Nelson Cragg-Uhler 1 Cragg-Uhler 2 Estrella Adjusted Estrella McFaddens LRI Veall-Zimmermann Akaike Information Criterion (AIC) Schwarz Criterion or Bayesian Information Criterion (BIC) The QLIM procedure analyzes univariate and multivariate limited dependent variable models where dependent variables take discrete values or dependent variables are observed only in a limited range of values. This procedure includes logit, probit, Tobit, and general simultaneous equations models. The QLIM procedure supports the following models:

Discrete Choice and Qualitative and Limited Dependent Variable Analysis ! 25

linear regression model with heteroscedasticity probit with heteroscedasticity logit with heteroscedasticity Tobit (censored and truncated) with heteroscedasticity Box-Cox regression with heteroscedasticity bivariate probit bivariate Tobit sample selection models multivariate limited dependent models The COUNTREG procedure provides regression models in which the dependent variable takes nonnegative integer count values. The COUNTREG procedure supports the following models: Poisson regression negative binomial regression with quadratic and linear variance functions zero inated Poisson (ZIP) model zero inated negative binomial (ZINB) model xed and random effect Poisson panel data models xed and random effect NB (negative binomial) panel data models The PANEL procedure deals with panel data sets that consist of time series observations on each of several cross-sectional units. The models and methods the PANEL procedure uses to analyze are as follows: one-way and two-way models xed and random effects autoregressive models the Parks method dynamic panel estimator the Da Silva method for moving-average disturbances


Regression with Autocorrelated and Heteroscedastic ErrorsThe AUTOREG procedure provides regression analysis and forecasting of linear models with autocorrelated or heteroscedastic errors. The AUTOREG procedure includes the following features: estimation and prediction of linear regression models with autoregressive errors any order autoregressive or subset autoregressive process optional stepwise selection of autoregressive parameters choice of the following estimation methods: exact maximum likelihood exact nonlinear least squares Yule-Walker iterated Yule-Walker

tests for any linear hypothesis that involves the structural coefcients restrictions for any linear combination of the structural coefcients forecasts with condence limits estimation and forecasting of ARCH (autoregressive conditional heteroscedasticity), GARCH (generalized autoregressive conditional heteroscedasticity), I-GARCH (integrated GARCH), E-GARCH (exponential GARCH), and GARCH-M (GARCH in mean) models combination of ARCH and GARCH models with autoregressive models, with or without regressors estimation and testing of general heteroscedasticity models variety of model diagnostic information including the following: autocorrelation plots partial autocorrelation plots Durbin-Watson test statistic and generalized Durbin-Watson tests to any order Durbin h and Durbin t statistics Akaike information criterion Schwarz information criterion tests for ARCH errors Ramseys RESET test Chow and PChow tests Phillips-Perron stationarity test CUSUM and CUMSUMSQ statistics

exact signicance levels (p-values) for the Durbin-Watson statistic embedded missing values

Simultaneous Systems Linear Regression ! 27

Simultaneous Systems Linear RegressionThe SYSLIN and ENTROPY procedures provide regression analysis of a simultaneous system of linear equations. The SYSLIN procedure includes the following features: estimation of parameters in simultaneous systems of linear equations full range of estimation methods including the following: ordinary least squares (OLS) two-stage least squares (2SLS) three-stage least squares (3SLS) iterated 3SLS (IT3SLS) seemingly unrelated regression (SUR) iterated SUR (ITSUR) limited-information maximum likelihood (LIML) full-information maximum likelihood (FIML) minimum expected loss (MELO) general K-class estimators weighted regression any number of restrictions for any linear combination of coefcients, within a single model or across equations tests for any linear hypothesis, for the parameters of a single model or across equations wide range of model diagnostics and statistics including the following: usual ANOVA tables and R-square statistics Durbin-Watson statistics standardized coefcients test for overidentifying restrictions residual plots standard errors and t tests covariance and correlation matrices of parameter estimates and equation errors predicted values, residuals, parameter estimates, and variance-covariance matrices saved in output SAS data sets other features of the SYSLIN procedure that enable you to do the following: impose linear restrictions on the parameter estimates


test linear hypotheses about the parameters write predicted and residual values to an output SAS data set write parameter estimates to an output SAS data set write the crossproducts matrix (SSCP) to an output SAS data set use raw data, correlations, covariances, or cross products as input The ENTROPY procedure supports the following models and features: generalized maximum entropy (GME) estimation generalized cross entropy (GCE) estimation normed moment generalized maximum entropy maximum entropy-based seemingly unrelated regression (MESUR) estimation pure inverse estimation estimation of parameters in simultaneous systems of linear equations Markov models unordered multinomial choice problems weighted regression any number of restrictions for any linear combination of coefcients, within a single model or across equations tests for any linear hypothesis, for the parameters of a single model or across equations

Linear Systems SimulationThe SIMLIN procedure performs simulation and multiplier analysis for simultaneous systems of linear regression models. The SIMLIN procedure includes the following features: reduced form coefcients interim multipliers total multipliers dynamic multipliers multipliers for higher order lags dynamic forecasts and simulations goodness-of-t statistics acceptance of the equation system coefcients estimated by the SYSLIN procedure as input

Polynomial Distributed Lag Regression ! 29

Polynomial Distributed Lag RegressionThe PDLREG procedure provides regression analysis for linear models with polynomial distributed (Almon) lags. The PDLREG procedure includes the following features: entry of any number of regressors as a polynomial lag distribution and the use of any number of covariates use of any order lag length and degree polynomial for lag distribution optional upper and lower endpoint restrictions specication of any number of linear restrictions on covariates option to repeat analysis over a range of degrees for the lag distribution polynomials support for autoregressive errors to any lag forecasts with condence limits

Nonlinear Systems Regression and SimulationThe MODEL procedure provides parameter estimation, simulation, and forecasting of dynamic nonlinear simultaneous equation models. The MODEL procedure includes the following features: nonlinear regression analysis for systems of simultaneous equations, including weighted nonlinear regression full range of parameter estimation methods including the following: nonlinear ordinary least squares (OLS) nonlinear seemingly unrelated regression (SUR) nonlinear two-stage least squares (2SLS) nonlinear three-stage least squares (3SLS) iterated SUR iterated 3SLS generalized method of moments (GMM) nonlinear full-information maximum likelihood (FIML) simulated method of moments (SMM) supports dynamic multi-equation nonlinear models of any size or complexity uses the full power of the SAS programming language for model denition, including lefthand-side expressions


hypothesis tests of nonlinear functions of the parameter estimates linear and nonlinear restrictions of the parameter estimates bounds imposed on the parameter estimates computation of estimates and standard errors of nonlinear functions of the parameter estimates estimation and simulation of ordinary differential equations (ODEs) vector autoregressive error processes and polynomial lag distributions easily specied for the nonlinear equations variance modeling (ARCH, GARCH, and others) computation of goal-seeking solutions of nonlinear systems to nd input values needed to produce target outputs dynamic, static, or n-period-ahead-forecast simulation modes simultaneous solution or single equation solution modes Monte Carlo simulation using parameter estimate covariance and across-equation residuals covariance matrices or user-specied random functions a variety of diagnostic statistics including the following model R-square statistics general Durbin-Watson statistics and exact p-values asymptotic standard errors and t tests rst-stage R-square statistics covariance estimates collinearity diagnostics simulation goodness-of-t statistics Theil inequality coefcient decompositions Theil relative change forecast error measures heteroscedasticity tests Godfrey test for serial correlation Hausman specication test Chow tests block structure and dependency structure analysis for the nonlinear system listing and cross-reference of tted model automatic calculation of needed derivatives by using exact analytic formula efcient sparse matrix methods used for model solution; choice of other solution methods Model denition, parameter estimation, simulation, and forecasting can be performed interactively in a single SAS session or models can also be stored in les and reused and combined in later runs.

ARIMA (Box-Jenkins) and ARIMAX (Box-Tiao) Modeling and Forecasting ! 31

ARIMA (Box-Jenkins) and ARIMAX (Box-Tiao) Modeling and ForecastingThe ARIMA procedure provides the identication, parameter estimation, and forecasting of autoregressive integrated moving-average (Box-Jenkins) models, seasonal ARIMA models, transfer function models, and intervention models. The ARIMA procedure includes the following features: complete ARIMA (Box-Jenkins) modeling with no limits on the order of autoregressive or moving-average processes model identication diagnostics including the following: autocorrelation function partial autocorrelation function inverse autocorrelation function cross-correlation function extended sample autocorrelation function minimum information criterion for model identication squared canonical correlations stationarity tests outlier detection intervention analysis regression with ARMA errors transfer function modeling with fully general rational transfer functions seasonal ARIMA models ARIMA model-based interpolation of missing values several parameter estimation methods including the following: exact maximum likelihood conditional least squares exact nonlinear unconditional least squares (ELS or ULS) prewhitening transformations forecasts and condence limits for all models forecasting tied to parameter estimation methods: nite memory forecasts for models estimated by maximum likelihood or exact nonlinear least squares methods and innite memory forecasts for models estimated by conditional least squares diagnostic statistics to help judge the adequacy of the model including the following:


Akaikes information criterion (AIC) Schwarzs Bayesian criterion (SBC or BIC) Box-Ljung chi-square test statistics for white-noise residuals autocorrelation function of residuals partial autocorrelation function of residuals inverse autocorrelation function of residuals automatic outlier detection

Vector Time Series AnalysisThe VARMAX procedure enables you to model the dynamic relationship both between the dependent variables and between the dependent and independent variables. The VARMAX procedure includes the following features: several modeling features: vector autoregressive model vector autoregressive model with exogenous variables vector autoregressive and moving-average model Bayesian vector autoregressive model vector error correction model Bayesian vector error correction model GARCH-type multivariate conditional heteroscedasticity models criteria for automatically determining AR and MA orders: Akaike information criterion (AIC) corrected AIC (AICC) Hannan-Quinn (HQ) criterion nal prediction error (FPE) Schwarz Bayesian criterion (SBC), also known as Bayesian information criterion (BIC) AR order identication aids: partial cross-correlations Yule-Walker estimates partial autoregressive coefcients partial canonical correlations testing the presence of unit roots and cointegration: Dickey-Fuller tests

State Space Modeling and Forecasting ! 33

Johansen cointegration test for nonstationary vector processes of integrated order one Stock-Watson common trends test for the possibility of cointegration among nonstationary vector processes of integrated order one Johansen cointegration test for nonstationary vector processes of integrated order two model parameter estimation methods: least squares (LS) maximum likelihood (ML) model checks and residual analysis using the following tests: Durbin-Watson (DW) statistics F test for autoregressive conditional heteroscedastic (ARCH) disturbance F test for AR disturbance Jarque-Bera normality test Portmanteau test seasonal deterministic terms subset models multiple regression with distributed lags dead-start model that does not have present values of the exogenous variables Granger-causal relationships between two distinct groups of variables innite order AR representation impulse response function (or innite order MA representation) decomposition of the predicted error covariances roots of the characteristic functions for both the AR and MA parts to evaluate the proximity of the roots to the unit circle contemporaneous relationships among the components of the vector time series forecasts conditional covariances for GARCH models

State Space Modeling and ForecastingThe STATESPACE procedure provides automatic model selection, parameter estimation, and forecasting of state space models. (State space models encompass an alternative general formulation of multivariate ARIMA models.) The STATESPACE procedure includes the following features:


multivariate ARIMA modeling by using the general state space representation of the stochastic process automatic model selection using Akaikes information criterion (AIC) user-specied state space models including restrictions transfer function models with random inputs any combination of simple and seasonal differencing; input series can be differenced to any order for any lag lengths forecasts with condence limits ability to save selected and tted model in a data set and reuse for forecasting wide range of output options including the ability to print any statistics concerning the data and their covariance structure, the model selection process, and the nal model t

Spectral AnalysisThe SPECTRA procedure provides spectral analysis and cross-spectral analysis of time series. The SPECTRA procedure includes the following features: efcient calculation of periodogram and smoothed periodogram using fast nite Fourier transform and Chirp-Z algorithms multiple spectral analysis, including raw and smoothed spectral and cross-spectral function estimates, with user-specied window weights choice of kernel for smoothing output of the following spectral estimates to a SAS data set: Fourier sine and cosine coefcients periodogram smoothed periodogram cospectrum quadrature spectrum amplitude phase spectrum squared coherency Fishers Kappa and Bartletts Kolmogorov-Smirnov test statistic for testing a null hypothesis of white noise

Seasonal Adjustment ! 35

Seasonal AdjustmentThe X11 procedure provides seasonal adjustment of time series by using the Census X-11 or X-11 ARIMA method. The X11 procedure is based on the U.S. Bureau of the Census X-11 seasonal adjustment program and also supports the X-11 ARIMA method developed by Statistics Canada. The X11 procedure includes the following features: decomposition of monthly or quarterly series into seasonal, trend, trading day, and irregular components both multiplicative and additive form of the decomposition all the features of the Census Bureau program support of the X-11 ARIMA method support of sliding spans analysis processing of any number of variables at once with no maximum length for a series computation of tests for stable, moving, and combined seasonality optional printing or storing in SAS data sets of the individual X11 tables that show the various components at different stages of the computation; full control over what is printed or output ability to project seasonal component one year ahead, which enables reintroduction of seasonal factors for an extrapolated series The X12 procedure provides seasonal adjustment of time series using the X-12 ARIMA method. The X12 procedure is based on the U.S. Bureau of the Census X-12 ARIMA seasonal adjustment program (version 0.3). It also supports the X-11 ARIMA method developed by Statistics Canada and the previous X-11 method of the U.S. Census Bureau. The X12 procedure includes the following features: decomposition of monthly or quarterly series into seasonal, trend, trading day, and irregular components support of multiplicative, additive, pseudo-additive, and log additive forms of decomposition support of the X-12 ARIMA method support of regARIMA modeling automatic identication of outliers support of TRAMO-based automatic model selection use of regressors to process missing values within the span of the series processing of any number of variables at once with no maximum length for a series


computation of tests for stable, moving, and combined seasonality spectral analysis of original, seasonally adjusted, and irregular series optional printing or storing in a SAS data set of the individual X11 tables that show the various components at different stages of the decomposition; full control over what is printed or output optional projection of seasonal component one year ahead, which enables reintroduction of seasonal factors for an extrapolated series

Structural Time Series Modeling and ForecastingThe UCM procedure provides a exible environment for analyzing time series data using structural time series models, also called unobserved components models (UCM). These models represent the observed series as a sum of suitably chosen components such as trend, seasonal, cyclical, and regression effects. You can use the UCM procedure to formulate comprehensive models that bring out all the salient features of the series under consideration. Structural models are applicable in the same situations where Box-Jenkins ARIMA models are applicable; however, the structural models tend to be more informative about the underlying stochastic structure of the series. The UCM procedure includes the following features: general unobserved components modeling where the models can include trend, multiple seasons and cycles, and regression effects maximum-likelihood estimation of the model parameters model diagnostics that include a variety of goodness-of-t statistics, and extensive graphical diagnosis of the model residuals forecasts and condence limits for the series and all the model components Model-based seasonal decomposition extensive plotting capability that includes the following: forecast and condence interval plots for the series and model components such as trend, cycles, and seasons diagnostic plots such as residual plot, residual autocorrelation plots, and so on seasonal decomposition plots such as trend, trend plus cycles, trend plus cycles plus seasons, and so on model-based interpolation of series missing values full sample (also called smoothed) estimates of the model components

Time Series Cross-Sectional Regression Analysis ! 37

Time Series Cross-Sectional Regression AnalysisThe TSCSREG procedure provides combined time series cross-sectional regression analysis. The TSCSREG procedure includes the following features: estimation of the regression parameters under several common error structures: Fuller and Battese method (variance component model) Wansbeek-Kapteyn method Parks method (autoregressive model) Da Silva method (mixed variance component moving-average model) one-way xed effects two-way xed effects one-way random effects two-way random effects any number of model specications unbalanced panel data for the xed or random-effects models variety of estimates and statistics including the following: underlying error components estimates regression parameter estimates standard errors of estimates t-tests R-square statistic correlation matrix of estimates covariance matrix of estimates autoregressive parameter estimate cross-sectional components estimates autocovariance estimates F tests of linear hypotheses about the regression parameters specication tests

Automatic Time Series ForecastingThe ESM procedure provides a quick way to generate forecasts for many time series or transactional data in one step by using exponential smoothing methods. All parameters associated with the forecasting model are optimized based on the data. You can use the following smoothing models:


simple double linear damped trend seasonal Winters method (additive and multiplicative) Additionally, PROC ESM can transform the data before applying the smoothing methods using any of these transformations: log square root logistic Box-Cox In addition to forecasting, the ESM procedure can also produce graphic output. The ESM procedure can forecast both time series data, whose observations are equally spaced at a specic time interval (for example, monthly, weekly), or transactional data, whose observations are not spaced with respect to any particular time interval. (Internet, inventory, sales, and similar data are typical examples of transactional data. For transactional data, the data are accumulated based on a specied time interval to form a time series.) The ESM procedure is a replacement for the older FORECAST procedure. ESM is often more convenient to use than PROC FORECAST but it supports only exponential smoothing models. The FORECAST procedure provides forecasting of univariate time series using automatic trend extrapolation. PROC FORECAST is an easy-to-use procedure for automatic forecasting and uses simple popular methods that do not require statistical modeling of the time series, such as exponential smoothing, time trend with autoregressive errors, and the Holt-Winters method. The FORECAST procedure supplements the powerful forecasting capabilities of the econometric and time series analysis procedures described previously. You can use PROC FORECAST when you have many series to forecast and you want to extrapolate trends without developing a model for each series. The FORECAST procedure includes the following features: choice of the following forecasting methods: EXPO methodexponential smoothing: single, double, triple, or Holt two-parameter smoothing exponential smoothing as an ARIMA Model

Time Series Interpolation and Frequency Conversion ! 39

WINTERS methodusing updating equations similar to exponential smoothing to t model parameters ADDWINTERS methodlike the WINTERS method except that the seasonal parameters are added to the trend instead of multiplied with the trend STEPAR methodstepwise autoregressive models with constant, linear, or quadratic trend and autoregressive errors to any order Holt-Winters forecasting method with constant, linear, or quadratic trend additive variant of the Holt-Winters method support for up to three levels of seasonality for Holt-Winters method: time-of-year, day-ofweek, or time-of-day ability to forecast any number of variables at once forecast condence limits for all methods

Time Series Interpolation and Frequency ConversionThe EXPAND procedure provides time interval conversion and missing value interpolation for time series. The EXPAND procedure includes the following features: conversion of time series frequency; for example, constructing quarterly estimates from annual series or aggregating quarterly values to annual values conversion of irregular observations to periodic observations interpolation of missing values in time series conversion of observation types; for example, estimate stocks from ows and vice versa. All possible conversions are supported between any of the following: beginning of period end of period period midpoint period total period average conversion of time series phase shift; for example, conversion between scal years and calendar years identifying observations including the following: identication of the time interval of the input values validation of the input data set observations computation of the ID values for the observations in the output data set


choice of four interpolation methods: cubic splines linear splines step functions simple aggregation ability to perform extrapolation by a linear projection of the trend of the cubic spline curve t to the input data ability to transform series before and after interpolation (or without interpolation) by using any of the following: constant shift or scale sign change or absolute value logarithm, exponential, square root, square, logistic, inverse logistic lags, leads, differences classical decomposition bounds, trims, reverse series centered moving, cumulative, or backward moving average centered moving, cumulative, or backward moving range centered moving, cumulative, or backward moving geometric mean centered moving, cumulative, or backward moving maximum centered moving, cumulative, or backward moving median centered moving, cumulative, or backward moving minimum centered moving, cumulative, or backward moving product centered moving, cumulative, or backward moving corrected sum of squares centered moving, cumulative, or backward moving uncorrected sum of squares centered moving, cumulative, or backward moving rank centered moving, cumulative, or backward moving standard deviation centered moving, cumulative, or backward moving sum centered moving, cumulative, or backward moving median centered moving, cumulative, or backward moving t-value centered moving, cumulative, or backward moving variance support for a wide range of time series frequencies: YEAR SEMIYEAR QUARTER MONTH SEMIMONTH

Trend and Seasonal Analysis on Transaction Databases ! 41

TENDAY WEEK WEEKDAY DAY HOUR MINUTE SECOND support for repeating of shifting the basic interval types to dene a great variety of different frequencies, such as scal years, biennial periods, work shifts, and so forth Refer to Chapter 3, Working with Time Series Data, and Chapter 4, Date Intervals, Formats, and Functions, for more information about time series data transformations.

Trend and Seasonal Analysis on Transaction DatabasesThe TIMESERIES procedure can accumulate transactional data to time series and perform trend and seasonal analysis on the accumulated time series. Time series analyses performed by the TIMESERIES procedure include the follows: descriptive statistics relevant for time series data seasonal decomposition and seasonal adjustment analysis correlation analysis cross-correlation analysis The TIMESERIES procedure includes the following features: ability to process large amounts of time-stamped transactional data statistical methods useful for large-scale time series analysis or (temporal) data mining output data sets stored in either a time series format (default) or a coordinate format (transposed) The TIMESERIES procedure is normally used to prepare data for subsequent analysis that uses other SAS/ETS procedures or other parts of the SAS system. The time series format is most useful when the data are to be analyzed with SAS/ETS procedures. The coordinate format is most useful when the data are to be analyzed with SAS/STAT procedures or SAS Enterprise MinerTM . (For example, clustering time-stamped transactional data can be achieved by using the results of TIMESERIES procedure with the clustering procedures of SAS/STAT and the nodes of SAS Enterprise Miner.)


Access to Financial and Economic DatabasesThe DATASOURCE procedure and the SAS/ETS data access interface LIBNAME Engines (SASECRSP, SASEFAME and SASEHAVR) provide seamless, efcient access to time series data from data les supplied by a variety of commercial and governmental data vendors. The DATASOURCE procedure includes the following features: support for data les distributed by the following data vendors: DRI/McGraw-Hill FAME Information Services HAVER ANALYTICS Standard & Poors Compustat Service Center for Research in Security Prices (CRSP) International Monetary Fund U.S. Bureau of Labor Statistics U.S. Bureau of Economic Analysis Organization for Economic Cooperation and Development (OECD) ability to select the series, frequency, time range, and cross sections of extracted data ability to create an output data set containing descriptive information on the series available in the data le ability to read EBCDIC data on ASCII systems and vice versa The SASECRSP interface LIBNAME engine includes the following features: enables random access to time series data residing in CRSPAccess databases provides a seamless interface between CRSP and SAS data processing uses the LIBNAME statement to enable you to specify which time series you would like to read from the CRSPAccess database, and how you would like to perform selection enables you access to CRSP Stock, CRSP/COMPUSTAT Merged (CCM) or CRSP Indices Data. provides convenient formats, informats, and functions for CRSP and SAS datetime conversions The SASEFAME interface LIBNAME engine includes the following features: provides SAS and FAME users exibility in accessing and processing time series data, case series, and formulas that reside in either a FAME database or a SAS data set

Access to Financial and Economic Databases ! 43

provides a seamless interface between FAME and SAS data processing uses the LIBNAME statement to enable you to specify which time series you would like to read from the FAME database enables you to convert the selected time series to the same time scale works with the SAS DATA step to perform further subsetting and to store the resulting time series into a SAS data set performs more analysis if desired either in the same SAS session or in another session at a later time supports the FAME CROSSLIST function for subsetting via BYGROUPS using the CROSSLIST= option you can use a FAME namelist that contains your BY variables for selection in the CROSSLIST you can use a SAS input dataset, INSET, that contains the BY selection variables along with the WHERE= option in your SASEFAME libref supports the use of FAME in a client/server environment that uses the FAME CHLI capability on your FAME server enables access to your FAME remote data when you specify the port number of the TCP/IP service that is dened for your FAME server and the node name of your FAME master server in your SASEFAME librefs physical path The SASEHAVR interface LIBNAME engine includes the following features: enables Windows users random access to economic and nancial data residing in a HAVER ANALYTICS Data Link Express (DLX) database the following types of HAVER data sets are available: United States Economic Indicators Specialized Databases Financial Indicators Industry Industrial Countries Emerging Markets International Organizations Forecasts and As Reported Data United States Regional enables you to limit the range of data that is read from the time series enables you to specify a desired conversion frequency. Start dates are recommended on the LIBNAME statement to help you save resources when processing large databases or when processing a large number of observations.


enables you to use the WHERE, KEEP, or DROP statements in your DATA step to further subset your data supports use of the SQL procedure to create a view of your resulting SAS data set

Spreadsheet Calculations and Financial Report GenerationThe COMPUTAB procedure generates tabular reports using a programmable data table. The COMPUTAB procedure is especially useful when you need both the power of a programmable spreadsheet and a report-generation system and you want to set up a program to run in batch mode and generate routine reports. The COMPUTAB procedure includes the following features: report generation facility for creating tabular reports such as income statements, balance sheets, and other row and column reports for analyzing business or time series data ability to tailor report format to almost any desired specication use of the SAS programming language to provide complete control of the calculation and format of each item of the report ability to report denit

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