MODELING IP WITH ARMA AND

VARJOHNS HOPKINS 2016

MACROECONOMETRICS FINAL PROJECT

PRESENTERS

Section 1 – Meagan Hawley

Section 2 – Emilio José Calle

Section 3 – Matías Costa

■ Introduction of Main Variable: Industrial Production Index (IPI)■ Section 1: Modelling IPI as an ARMA Process ■ Section 2: Modelling of IPI with other Explanatory Variables ■ Section 3: Unemployment Forecasting in VAR

Report Components

The Variable: Industrial Production Index

■ The monthly Industrial Production Index (IP) is an economic indicator from the Federal Reserve Board that measures the real production of output from manufacturing, mining, and utilities such as electric and gas.

■  Data for the index are pulled from the Bureau of Labor Statistics and various trade associations on a monthly basis. IP is computed as a Fisher index with weights based on annual estimates of value added and the base year (currently 2012) set to 100.

■  The Fisher index is calculated by taking the geometric mean of the Laspeyres and Paasche indices

■ Many investors use the IP index of several industries in order to examine the growth in the industry. Generally, when the indicator grows every month, it is a positive sign that shows the industry is performing well.

Section 1: Modelling IPI in ARMA

Plotting IPI

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CORRELOGRAM FOR THE INDUSTRIAL PRODUCTION INDEX

COMMENT ON THE DATAThis time series appears stationary as it reflects a constant variance and mean over time. Specifically, the data appear to fluctuate along a constant mean of 0. The floor and ceiling of these series range from 5 to -5, except when you look at the 2008 financial recession you can see that the IP dropped down past -15.

This is consistent with the way this variable is built, as explained in the introduction at the beginning of this report.

DECIDE ON AN ARMA(P,Q) MODEL BASED ON (SIC, BIC) AND SIMPLICITY

We selected an ARMA(4,11) for our model based on low SIC and BIC values as well as the simplicity of the p,q values.

As demonstrated in the “ARMA Criteria Table” below, an ARMA(4,11) has both the lowest SIC(AIC) and BIC values of all the ARMA(p,q) combinations.

Additionally, the ARMA(4,11) is the simplest model when compared to other ARMA models that have similar, but slightly higher SIC and BIC values. If one of the other ARMA combinations revealed slightly higher SIC and BIC values, but offered a lower-order model, we would have considered that one over the ARMA(4,11).

In this case, however, the ARMA(4,11) offers us the best fit based on all three SIC, BIC and model simplicity criteria. The reason for the high-order MA component in this model is because the Industrial Production variable is defined as the growth rate year on year, leading to a strong MA presence.

ARMA Comparative TablesSIC/AIC AR

MA -Values- 4 5 610 1.475 1.567 1.43711 1.347 1.349 1.35312 3.935 4.243 1.348

BIC ARMA -Values- 4 5 6

10 1.598 1.698 1.57511 1.478 1.488 1.49912 4.073 4.389 1.502

ARMA Criteria Graph

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Akaike Information Criteria (top 20 models)

ACTUAL VS. FITTED GRAPHS

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Residual Actual Fitted

MODEL AND DYNAMIC FORECAST FOR THE NEXT 5 YEARS

Section 2: IPI and Other Variables

INCLUDE THE OTHER 4 VARIABLES AS EXPLANATORY VARIABLES

What can be seen below is the different AR-MA combinations that were tried out to select the best-fitting model for the data set.

The first one tested was the base AR(4) MA(11) found in the previous section using only IPI and its autoregressions. Registering the results it can be seen that the AIC is 1.617118 and SIC 1.892762, but other combinations of AR and MA gave better fitting results.

AR(5) MA(12) being the best fitting one with AIC = 1.470070 and SIC= 1.796323.Thus this model was selected for the multivariable case.

R-squared 0.982097    Mean dependent var 1.441786Adjusted R-squared 0.980637    S.D. dependent var 3.375664S.E. of regression 0.469727    Akaike info criterion 1.470070Sum squared resid 102.8199    Schwarz criterion 1.796323Log likelihood -332.1927    Hannan-Quinn criter. 1.598037F-statistic 672.7113    Durbin-Watson stat 2.011893Prob(F-statistic) 0.000000      

RESULTS FOR ARMA (5,12)

MODEL UP TO 2013M12 AND DYNAMIC FORECAST UP TO 2015

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I II III IV I II III IV I II III IV I II III IV I II

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ip IPF UP_IP LB_IP

Section 3: IRF of each of the 5 variables to ashock in IPI

SHOW HOW THE 5 VARIABLES RESPOND TO A STANDARDIZED SHOCK TO THE UNEMPLOYMENT RATE