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Applied Econometric Applied Econometric Time SeriesTime SeriesThird EditionThird Edition

Walter Enders, University of Alabama

Copyright © 2010 John Wiley & Sons, Inc.

CHAPTER 2CHAPTER 2STATIONARY TIME-STATIONARY TIME-SERIESSERIESMODELSMODELS

1. STOCHASTIC 1. STOCHASTIC DIFFERENCE EQUATION DIFFERENCE EQUATION MODELSMODELS

2. ARMA MODELS2. ARMA MODELS

3. STATIONARITY3. STATIONARITYStationarity Restrictions for an AR(1) Process

4. STATIONARITY 4. STATIONARITY RESTRICTIONSRESTRICTIONSFOR AN ARMA(p, q) FOR AN ARMA(p, q) MODELMODELStationarity Restrictions for the Autoregressive Coefficients

5. THE 5. THE AUTOCORRELATION AUTOCORRELATION FUNCTION FUNCTION

The Autocorrelation Function of an AR(2) Process

The Autocorrelation Function of an MA(1) Process

The Autocorrelation Function of an ARMA(1, 1) Process

6. THE PARTIAL 6. THE PARTIAL AUTOCORRELATION AUTOCORRELATION FUNCTION FUNCTION

7. SAMPLE 7. SAMPLE AUTOCORRELATIONSAUTOCORRELATIONSOF STATIONARY SERIESOF STATIONARY SERIES

Model Selection CriteriaEstimation of an AR(1) ModelEstimation of an ARMA(1, 1) Model

Estimation of an AR(2) Model

8. BOX–JENKINS MODEL 8. BOX–JENKINS MODEL SELECTIONSELECTION

ParsimonyStationarity and InvertibilityGoodness of FitPost-Estimation Evaluation

9. PROPERTIES OF 9. PROPERTIES OF FORECASTSFORECASTS

Higher-Order ModelsForecast Evaluation

◦The Granger–Newbold Test◦The Diebold-Mariano Test

10. A MODEL OF THE 10. A MODEL OF THE INTEREST RATE INTEREST RATE SPREADSPREADOut-of-Sample Forecasts

11. SEASONALITY11. SEASONALITY

Models of Seasonal DataSeasonal Differencing

12. PARAMETER 12. PARAMETER INSTABILITY AND INSTABILITY AND STRUCTURAL CHANGESTRUCTURAL CHANGE

Testing for Structural ChangeEndogenous BreaksParameter InstabilityAn Example of a Break

13. SUMMARY AND 13. SUMMARY AND CONCLUSIONSCONCLUSIONS

APPENDIX 2.1: APPENDIX 2.1: ESTIMATION OF AN ESTIMATION OF AN MA(1) PROCESSMA(1) PROCESS

APPENDIX 2.2: MODEL APPENDIX 2.2: MODEL SELECTION CRITERIASELECTION CRITERIA

The Finite Prediction Error (FPE) Criterion

The AIC and the SBC