This document discusses modeling industrial production (IP) using ARMA and VAR models. It contains the following key points: 1. An ARMA(4,11) model is selected to model IP based on it having the lowest SIC and BIC values as well as a simple parameterization. The model fits the data well with stationary fluctuations around a constant mean. 2. Additional explanatory variables of housing starts, industrial materials, manufacturing & trade sales, and unemployment are added to the ARMA(5,12) model, improving the fit. 3. The multivariate model is used to generate dynamic forecasts of IP through 2015. Impulse response functions show how the 5 variables respond to a standardized shock in

1. MODELING IPWITH
ARMA ANDVAR
JOHNS HOPKINS 2016
MACROECONOMETRICS FINAL PROJECT

2. PRESENTERS
Section 1 – Meagan Hawley
Section 2 – Emilio José Calle
Section 3 – Matías Costa

3. ■ Introduction of MainVariable: Industrial Production Index (IPI)
■ Section 1: Modelling IPI as an ARMA Process
■ Section 2: Modelling of IPI with other ExplanatoryVariables
■ Section 3: Unemployment Forecasting inVAR

4. ■ 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.

5. Section 1:
Modelling IPI in ARMA

6. Plotting IPI
-20
-15
-10
-5
0
5
10
1975 1980 1985 1990 1995 2000 2005 2010 2015
ip

7. CORRELOGRAM
FORTHE
INDUSTRIAL
PRODUCTION
INDEX

8. COMMENT ONTHE DATA
This 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.

9. 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.

10. ARMA ComparativeTables
SIC/AIC AR
MA
-Values- 4 5 6
10 1.475 1.567 1.437
11 1.347 1.349 1.353
12 3.935 4.243 1.348
BIC AR
MA
-Values- 4 5 6
10 1.598 1.698 1.575
11 1.478 1.488 1.499
12 4.073 4.389 1.502

11. ARMA Criteria Graph
1.34
1.35
1.36
1.37
1.38
1.39
1.40
1.41
1.42
(4,11)(0,0)
(6,12)(0,0)
(5,11)(0,0)
(7,11)(0,0)
(6,11)(0,0)
(7,12)(0,0)
(8,11)(0,0)
(3,11)(0,0)
(1,12)(0,0)
(9,11)(0,0)
(12,11)(0,0)
(10,12)(0,0)
(8,12)(0,0)
(11,12)(0,0)
(10,11)(0,0)
(9,12)(0,0)
(11,11)(0,0)
(2,11)(0,0)
(3,12)(0,0)
(12,10)(0,0)
Akaike Information Criteria (top 20 models)

12. ACTUALVS. FITTED GRAPHS
-4
-3
-2
-1
0
1
2
-20
-15
-10
-5
0
5
10
1975 1980 1985 1990 1995 2000 2005 2010 2015
Residual Actual Fitted

13. MODEL AND
DYNAMIC
FORECAST FOR
THE NEXT 5YEARS

14. Section 2:
IPI and Other Variables

15. 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.

16. R-squared 0.982097 Mean dependent var 1.441786
Adjusted R-squared 0.980637 S.D. dependent var 3.375664
S.E. of regression 0.469727 Akaike info criterion 1.470070
Sum squared resid 102.8199 Schwarz criterion 1.796323
Log likelihood -332.1927 Hannan-Quinn criter. 1.598037
F-statistic 672.7113 Durbin-Watson stat 2.011893
Prob(F-statistic) 0.000000
RESULTS FOR ARMA (5,12)

17. MODEL UP TO 2013M12 AND
DYNAMIC FORECAST UP TO 2015
-1
0
1
2
3
4
5
6
7
8
I II III IV I II III IV I II III IV I II III IV I II
2011 2012 2013 2014 2015
ip IPF UP_IP LB_IP

18. Section 3: IRF of each
of the 5 variables to a
shock in IPI

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