arma and var modelling of industrial production in america

JOHNS HOPKINS AAP AUGUST 2016

Modeling ARMA and VAR MACROECONOMETRICS FINAL PROJECT

Johns Hopkins AAP Matías Costa – Maegan Hawley – Emilio José Calle

MACROECONOMETRICS FINAL PROJECT AUGUST 2016

Modeling ARMA and VAR 2

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



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:

where is Laspeyres' index and is Paasche's index. And P is the Industrial Price Index.

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.

Source: http://www.federalreserve.gov/Releases/g17/About.htm



1a. PLOT THE DATA FOR THE INDUSTRIAL PRODUCTION INDEX:

-20

-15

-10

-5

0

5

10

1975 1980 1985 1990 1995 2000 2005 2010 2015

ip



1b. PLOT THE CORRELOGRAM FOR THE INDUSTRIAL PRODUCTION INDEX:



2. COMMENT ON THE 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.

3. DECIDE ON AN ARMA(P,Q) MODEL BASED ON _T (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.

SUMMARY:

Automatic ARIMA Forecasting Selected dependent variable: IP Date: 08/06/16 Time: 10:39 Sample: 1973M01 2019M12 Included observations: 510 Forecast length: 0

Number of estimated ARMA models: 169 Number of non-converged estimations: 0 Selected ARMA model: (4,11)(0,0)

AIC value: 1.34747400898



Equation Output

Dependent Variable: IP

Method: ARMA Maximum Likelihood (BFGS)

Date: 08/06/16 Time: 10:39

Sample: 1973M01 2015M06

Included observations: 510

Convergence achieved after 93 iterations

Coefficient covariance computed using outer product of gradients Variable Coefficient Std. Error t-Statistic Prob. C 1.443722 0.781700 1.846900 0.0654

AR(1) 0.164718 0.036776 4.478924 0.0000

AR(2) 0.153853 0.050182 3.065880 0.0023

AR(3) 0.186425 0.042044 4.434039 0.0000

AR(4) 0.124788 0.046207 2.700646 0.0072

MA(1) 0.975557 1.190018 0.819783 0.4127

MA(2) 0.984597 1.512608 0.650926 0.5154

MA(3) 0.986381 1.967560 0.501322 0.6164

MA(4) 0.978262 1.717025 0.569742 0.5691

MA(5) 0.993363 1.208197 0.822186 0.4114

MA(6) 0.993364 0.929092 1.069177 0.2855

MA(7) 0.978258 1.607138 0.608696 0.5430

MA(8) 0.986382 1.815927 0.543184 0.5872

MA(9) 0.984599 1.700871 0.578879 0.5629

MA(10) 0.975557 1.431133 0.681668 0.4958

MA(11) 0.999988 1.463988 0.683058 0.4949

SIGMASQ 0.222078 0.712393 0.311735 0.7554 R-squared 0.980388 Mean dependent var 1.466513

Adjusted R-squared 0.979751 S.D. dependent var 3.368342

S.E. of regression 0.479308 Akaike info criterion 1.490148

Sum squared resid 113.2599 Schwarz criterion 1.631295

Log likelihood -362.9877 Hannan-Quinn criter. 1.545487

F-statistic 1540.278 Durbin-Watson stat 1.986116

Prob(F-statistic) 0.000000 Inverted AR Roots .83 -.09-.55i -.09+.55i -.48

Inverted MA Roots .87+.50i .87-.50i .50-.86i .50+.86i

.00+1.00i .00-1.00i -.49-.87i -.49+.87i

-.87+.50i -.87-.50i -1.00



ARMA Criteria Table

Model Selection Criteria Table


Date: 08/06/16 Time: 10:39

Sample: 1973M01 2019M12


Model LogL AIC* BIC HQ

(4,11)(0,0) -362.987671 1.347474 1.478141 1.398480

(6,12)(0,0) -360.245493 1.348388 1.502114 1.408395

(5,11)(0,0) -362.526922 1.349386 1.487739 1.403393

(7,11)(0,0) -361.413988 1.352532 1.506257 1.412539

(6,11)(0,0) -362.454659 1.352676 1.498715 1.409683

(7,12)(0,0) -360.813764 1.353950 1.515361 1.416957

(8,11)(0,0) -361.383645 1.355970 1.517382 1.418978

(3,11)(0,0) -366.428370 1.356129 1.479109 1.404135

(1,12)(0,0) -367.962481 1.358023 1.473317 1.403028

(9,11)(0,0) -361.072661 1.358414 1.527512 1.424421

(12,11)(0,0) -358.088969 1.358472 1.550628 1.433480

(10,12)(0,0) -359.112917 1.358556 1.543027 1.430565

(8,12)(0,0) -361.338976 1.359358 1.528456 1.425366

(11,12)(0,0) -358.350739 1.359400 1.551556 1.434409

(10,11)(0,0) -361.001097 1.361706 1.538490 1.430714

(9,12)(0,0) -361.050238 1.361880 1.538664 1.430888

(11,11)(0,0) -360.282989 1.362706 1.547176 1.434714

(2,11)(0,0) -376.873152 1.389621 1.504915 1.434626

(3,12)(0,0) -375.880800 1.393194 1.523861 1.444200

(12,10)(0,0) -373.851643 1.410821 1.595292 1.482830

(10,10)(0,0) -376.744712 1.413988 1.583086 1.479996

(11,10)(0,0) -376.670631 1.417272 1.594056 1.486280

(1,11)(0,0) -388.914152 1.428774 1.536381 1.470778

(7,10)(0,0) -383.986963 1.429032 1.575071 1.486038

(8,10)(0,0) -383.033685 1.429197 1.582923 1.489204

(6,10)(0,0) -387.199921 1.436879 1.575232 1.490885

(0,12)(0,0) -395.155250 1.450905 1.558513 1.492910

(4,10)(0,0) -399.991194 1.475146 1.598126 1.523152

(0,11)(0,0) -408.435179 1.494451 1.594372 1.533456

(12,8)(0,0) -408.595301 1.526934 1.696032 1.592941

(10,8)(0,0) -411.767177 1.531089 1.684815 1.591096

(6,9)(0,0) -415.770467 1.534647 1.665314 1.585653

(12,9)(0,0) -409.891168 1.535075 1.711859 1.604083

(5,9)(0,0) -418.053636 1.539197 1.662178 1.587203

(9,8)(0,0) -415.496945 1.540769 1.686808 1.597776

(7,9)(0,0) -417.201359 1.543267 1.681620 1.597274

(12,6)(0,0) -417.673147 1.552032 1.705758 1.612039

(8,8)(0,0) -421.800649 1.559577 1.697930 1.613583

(5,10)(0,0) -425.000821 1.567379 1.698045 1.618385

(7,8)(0,0) -425.492159 1.569121 1.699788 1.620127

(4,9)(0,0) -427.848888 1.570386 1.685680 1.615391

(5,8)(0,0) -429.681638 1.576885 1.692179 1.621890

(6,8)(0,0) -428.706766 1.576974 1.699955 1.624980

(3,9)(0,0) -432.941175 1.584898 1.692506 1.626903

(10,9)(0,0) -426.119242 1.585529 1.746941 1.648537

(3,10)(0,0) -432.941020 1.588443 1.703737 1.633449

(11,7)(0,0) -428.799780 1.591489 1.745214 1.651496

(11,9)(0,0) -427.454443 1.593810 1.762908 1.659818

(8,7)(0,0) -437.246023 1.610801 1.741468 1.661807

(9,7)(0,0) -437.222781 1.614265 1.752618 1.668271

(11,6)(0,0) -436.747639 1.616126 1.762165 1.673133

(12,5)(0,0) -438.214578 1.621328 1.767367 1.678335

(11,5)(0,0) -439.370939 1.621883 1.760236 1.675889

(9,9)(0,0) -438.047082 1.624280 1.778006 1.684287

(8,9)(0,0) -440.375478 1.628991 1.775030 1.685998

(10,6)(0,0) -442.859748 1.634254 1.772607 1.688261

(12,4)(0,0) -444.107642 1.638680 1.777032 1.692686

(3,8)(0,0) -451.578838 1.647443 1.747364 1.686447

(2,10)(0,0) -451.966498 1.652363 1.759971 1.694368

(11,8)(0,0) -445.304276 1.653561 1.814973 1.716569

(1,10)(0,0) -454.864348 1.659093 1.759015 1.698098

(2,8)(0,0) -456.084675 1.659875 1.752110 1.695879

(10,5)(0,0) -452.676231 1.665519 1.796185 1.716524

(11,4)(0,0) -453.171503 1.667275 1.797941 1.718281

(7,6)(0,0) -460.072167 1.684653 1.799947 1.729658

(8,6)(0,0) -459.774204 1.687143 1.810123 1.735148

(2,9)(0,0) -462.792840 1.687209 1.787130 1.726213

(9,6)(0,0) -459.654250 1.690263 1.820930 1.741269

(6,5)(0,0) -464.269208 1.692444 1.792365 1.731449

(9,5)(0,0) -461.461571 1.693126 1.816106 1.741132

(7,5)(0,0) -463.789247 1.694288 1.801896 1.736293

(6,6)(0,0) -463.844291 1.694483 1.802091 1.736488

(6,7)(0,0) -463.278773 1.696024 1.811318 1.741029

(10,4)(0,0) -462.306959 1.696124 1.819104 1.744130

(7,7)(0,0) -462.518762 1.696875 1.819855 1.744881

(1,9)(0,0) -467.157535 1.699140 1.791375 1.735144

(12,3)(0,0) -463.820215 1.705036 1.835703 1.756042

(7,4)(0,0) -469.082479 1.709512 1.809434 1.748517

(10,7)(0,0) -463.127710 1.709673 1.855712 1.766679

(10,3)(0,0) -467.268605 1.710172 1.825466 1.755178

(8,4)(0,0) -468.340025 1.710426 1.818033 1.752431

(9,4)(0,0) -467.707488 1.711729 1.827023 1.756734

(11,3)(0,0) -467.257505 1.713679 1.836659 1.761685

(8,5)(0,0) -469.530024 1.718192 1.833486 1.763197

(9,3)(0,0) -474.725815 1.733070 1.840678 1.775075

(4,7)(0,0) -476.268471 1.734995 1.834916 1.773999

(5,4)(0,0) -480.203934 1.741858 1.826407 1.774862

(5,6)(0,0) -478.850795 1.744152 1.844073 1.783156

(6,4)(0,0) -480.203295 1.745402 1.837637 1.781406

(5,5)(0,0) -480.203357 1.745402 1.837637 1.781406

(5,7)(0,0) -479.726171 1.750802 1.858410 1.792807

(10,2)(0,0) -480.226765 1.752577 1.860185 1.794582

(11,2)(0,0) -480.087788 1.755630 1.870924 1.800636

(1,8)(0,0) -485.085941 1.759170 1.843719 1.792174

(2,7)(0,0) -485.869889 1.761950 1.846499 1.794954

(9,2)(0,0) -484.582778 1.764478 1.864399 1.803482

(5,3)(0,0) -488.789099 1.768756 1.845618 1.798759

(8,2)(0,0) -487.804321 1.772356 1.864591 1.808360

(3,7)(0,0) -492.800820 1.790074 1.882309 1.826078

(8,3)(0,0) -494.943302 1.801217 1.901139 1.840222

(4,5)(0,0) -497.227028 1.802224 1.886772 1.835227

(4,4)(0,0) -498.701906 1.803907 1.880770 1.833911

(4,6)(0,0) -497.466900 1.806620 1.898855 1.842624



(4,2)(0,0) -503.400878 1.813478 1.874968 1.837481

(3,6)(0,0) -500.463029 1.813699 1.898248 1.846703

(3,4)(0,0) -502.589754 1.814148 1.883324 1.841151

(4,3)(0,0) -504.470318 1.820817 1.889993 1.847820

(2,6)(0,0) -504.432467 1.824229 1.901091 1.854232

(3,3)(0,0) -506.461382 1.824331 1.885821 1.848334

(12,1)(0,0) -502.733729 1.835935 1.951229 1.880940

(3,2)(0,0) -513.642005 1.846248 1.900052 1.867251

(2,3)(0,0) -516.568962 1.856628 1.910431 1.877630

(2,4)(0,0) -515.947286 1.857969 1.919459 1.881972

(5,1)(0,0) -516.265679 1.859098 1.920588 1.883101

(6,0)(0,0) -516.282596 1.859158 1.920648 1.883161

(4,1)(0,0) -517.445740 1.859737 1.913541 1.880739

(2,2)(0,0) -518.589611 1.860247 1.906364 1.878249

(2,5)(0,0) -515.666931 1.860521 1.929697 1.887524

(5,0)(0,0) -517.673534 1.860544 1.914348 1.881547

(7,0)(0,0) -516.199895 1.862411 1.931587 1.889414

(6,1)(0,0) -516.212731 1.862456 1.931633 1.889460

(5,2)(0,0) -516.220101 1.862483 1.931659 1.889486

(3,1)(0,0) -519.231552 1.862523 1.908641 1.880525

(1,7)(0,0) -515.466520 1.863356 1.940219 1.893360

(3,5)(0,0) -515.942954 1.865046 1.941909 1.895049

(8,0)(0,0) -516.193849 1.865936 1.942798 1.895939

(7,1)(0,0) -516.197813 1.865950 1.942812 1.895953

(6,2)(0,0) -516.208187 1.865986 1.942849 1.895990

(2,1)(0,0) -521.327816 1.866411 1.904842 1.881412

(1,6)(0,0) -517.441093 1.866812 1.935989 1.893816

(9,0)(0,0) -516.154370 1.869342 1.953891 1.902346

(8,1)(0,0) -516.192084 1.869475 1.954024 1.902479

(6,3)(0,0) -516.213180 1.869550 1.954099 1.902554

(10,0)(0,0) -515.401466 1.870218 1.962453 1.906222

(11,0)(0,0) -515.346987 1.873571 1.973492 1.912575

(10,1)(0,0) -515.381501 1.873693 1.973615 1.912698

(12,0)(0,0) -515.318104 1.877015 1.984622 1.919019

(11,1)(0,0) -515.346486 1.877115 1.984723 1.919120

(1,5)(0,0) -523.894381 1.886150 1.947640 1.910153

(4,0)(0,0) -526.078151 1.886802 1.932920 1.904804

(1,4)(0,0) -528.725419 1.899736 1.953539 1.920738

(0,9)(0,0) -530.709045 1.920954 2.005503 1.953958

(3,0)(0,0) -538.362824 1.926819 1.965250 1.941820

(1,3)(0,0) -545.539618 1.955814 2.001932 1.973816

(0,10)(0,0) -541.688277 1.963434 2.055669 1.999438

(0,8)(0,0) -547.649724 1.977481 2.054344 2.007485

(1,2)(0,0) -553.672424 1.981108 2.019539 1.996110

(2,0)(0,0) -555.119109 1.982692 2.013437 1.994693

(0,7)(0,0) -551.626866 1.988039 2.057215 2.015042

(0,6)(0,0) -559.042711 2.010790 2.072280 2.034793

(1,1)(0,0) -563.691553 2.013091 2.043836 2.025092

(1,0)(0,0) -580.820379 2.070285 2.093344 2.079286

(0,5)(0,0) -620.959701 2.226807 2.280611 2.247810

(0,4)(0,0) -666.562008 2.384972 2.431089 2.402974

(0,3)(0,0) -773.653139 2.761181 2.799613 2.776183

(2,12)(0,0) -815.501117 2.948586 3.071566 2.996591

(0,2)(0,0) -886.835544 3.158991 3.189736 3.170993

(9,10)(0,0) -902.277268 3.274033 3.435444 3.337040

(0,1)(0,0) -1044.900153 3.715958 3.739017 3.724959

(7,3)(0,0) -1062.858918 3.811556 3.903792 3.847561

(4,12)(0,0) -1091.544748 3.934556 4.072909 3.988562

(4,8)(0,0) -1105.261357 3.969012 4.076620 4.011017

(12,12)(0,0) -1131.375671 4.104169 4.304012 4.182178

(12,7)(0,0) -1139.412641 4.114938 4.276350 4.177946

(5,12)(0,0) -1177.395555 4.242537 4.388576 4.299544

(9,1)(0,0) -1198.855069 4.293812 4.386047 4.329816

(7,2)(0,0) -1207.550137 4.321100 4.405649 4.354104

(0,0)(0,0) -1342.512689 4.767775 4.783148 4.773776

(12,2)(0,0) -1328.701646 4.768446 4.891426 4.816451

ARMA Criteria Graph

1.34

1.35

1.36

1.37

1.38

1.39

1.40

1.41

1.42

(4,1

1)(

0,0

)

(6,1

2)(

0,0

)

(5,1

1)(

0,0

)

(7,1

1)(

0,0

)

(6,1

1)(

0,0

)

(7,1

2)(

0,0

)

(8,1

1)(

0,0

)

(3,1

1)(

0,0

)

(1,1

2)(

0,0

)

(9,1

1)(

0,0

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(12,1

1)(

0,0

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(10,1

2)(

0,0

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(8,1

2)(

0,0

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(11,1

2)(

0,0

)

(10,1

1)(

0,0

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(9,1

2)(

0,0

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(11,1

1)(

0,0

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(2,1

1)(

0,0

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(3,1

2)(

0,0

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(12,1

0)(

0,0

)

Akaike Information Criteria (top 20 models)



ARMA Comparative Tables

4. SHOW RESIDUAL DIAGNOSTICS THAT VALIDATE YOUR CHOICE OF MODEL (RESIDUAL

CORRELOGRAMS, Q-TEST, ETC).

The plot of the residuals (below) shows no discernable pattern, a constant variance and an expected mean of zero. In other words, the residuals look like white noise, which is an indication that our chosen model is a good fit to the data. The plot also shows that the actual vs. fitted values are a very close match.

The correlogram of the residuals show that the bars for both the Autocorrelation Function (ACF) and the Partial Autocorrelation Function (PCF) are close to zero with no pattern to them. These results suggest that there is no correlation between the residuals, which further supports our chosen model.

Lastly, when we look at the Q-stats, we can see that all the associated p-values are all much greater than 0.05 meaning we fail to reject the null hypothesis that there is no serial correlation between residuals. These results are good news for our model since failing to reject the null hypothesis supports the case that there is no serial correlation between the residuals. If the p-values had been less than 0.05, it would have suggested there was serial correlation between the residuals thus indicating a need to reevaluate our model.

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



Actual vs. 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

Residual Correlograms and Q-Test



5. ESTIMATE THE MODEL UP TO THE LATEST OBSERVATION. THEN DO A DYNAMIC FORECAST

FOR THE NEXT 5 YEARS. INCLUDE CONFIDENCE INTERVALS.

-8

-6

-4

-2

0

2

4

6

8

10

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

2015 2016 2017 2018 2019

IPF ± 2 S.E.

Forecast: IPF

Actual: IP

Forecast sample: 2015M06 2019M12


Root Mean Squared Error 0.085313

Mean Absolute Error 0.085313

Mean Abs. Percent Error 32.51241

A dynamic forecast is one that does not update its knowledge after each period, which is why we

see here that the forecast trends back towards the mean.



6. Next, include the other 4 variables as explanatory variables. You will need to decide on

model { how many lags (p) of each variable, and how many MA components (q) to keep. Here

is my suggestion, start with the p and q you used in step 2 on this list. For example, if you

modeled your main variable as an ARMA(6,2), then use 6 lags for all of the explanatory

variables and keep the MA(2) structure. Use the same lag p for all the explanatory variables.

Then, as usual, try different p's and q's and see how SIC and BIC change. Decide on a model.

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.




Method: ARMA Maximum Likelihood (OPG - BHHH)

Date: 08/06/16 Time: 12:49

Sample: 1973M05 2015M06


Convergence not achieved after 500 iterations

Coefficient covariance computed using outer product of gradients

Variable Coefficient Std. Error t-Statistic Prob.

IP(-1) 1.626231 0.063603 25.56848 0.0000

IP(-2) -1.139602 0.094570 -12.05032 0.0000

IP(-3) 0.827362 0.086416 9.574186 0.0000

IP(-4) -0.401640 0.043961 -9.136367 0.0000

FFR(-1) 0.052233 0.035180 1.484727 0.1383

FFR(-2) -0.093678 0.059476 -1.575072 0.1159

FFR(-3) 0.038771 0.059255 0.654306 0.5132

FFR(-4) 0.020148 0.033260 0.605755 0.5450

PCEINFLATION(-1) 0.132827 0.079418 1.672495 0.0951

PCEINFLATION(-2) -0.325140 0.170335 -1.908830 0.0569

PCEINFLATION(-3) 0.253194 0.180984 1.398984 0.1625

PCEINFLATION(-4) -0.091053 0.088184 -1.032543 0.3023

EBP(-1) -0.182081 0.054737 -3.326446 0.0009

EBP(-2) -0.004094 0.080632 -0.050777 0.9595

EBP(-3) -0.136642 0.077741 -1.757671 0.0795

EBP(-4) 0.013316 0.062077 0.214512 0.8302

UNEMP(-1) -0.216873 0.123165 -1.760830 0.0789

UNEMP(-2) 0.058144 0.185887 0.312792 0.7546

UNEMP(-3) -0.085399 0.185975 -0.459193 0.6463

UNEMP(-4) 0.256941 0.111862 2.296934 0.0221

C 0.094166 0.107693 0.874395 0.3823

MA(1) -0.789370 3.128521 -0.252314 0.8009

MA(2) 0.911486 8.758849 0.104065 0.9172

MA(3) -0.762165 9.246236 -0.082430 0.9343

MA(4) 0.753322 2.200428 0.342353 0.7322

MA(5) -0.693954 1.843193 -0.376496 0.7067

MA(6) 0.750070 7.817659 0.095946 0.9236

MA(7) -0.756369 8.002078 -0.094522 0.9247

MA(8) 0.901179 10.02509 0.089892 0.9284

MA(9) -0.723709 8.908408 -0.081239 0.9353

MA(10) 0.972506 9.834049 0.098892 0.9213

MA(11) -0.715011 6.092958 -0.117350 0.9066

SIGMASQ 0.244935 1.517994 0.161354 0.8719

R-squared 0.978442 Mean dependent var 1.446557






Prob(F-statistic) 0.000000

Inverted MA Roots .84-.43i .84+.43i .82 .51+.86i

.51-.86i -.00-1.00i -.00+1.00i -.48-.86i

-.48+.86i -.88-.48i -.88+.48i




Method: ARMA Maximum Likelihood (OPG - BHHH)

Date: 08/06/16 Time: 13:11

Sample: 1973M06 2015M06


Convergence not achieved after 500 iterations

Coefficient covariance computed using outer product of gradients

Variable Coefficient Std. Error t-Statistic Prob.

IP(-1) 0.913110 0.082557 11.06042 0.0000

IP(-2) 0.040925 0.071919 0.569050 0.5696

IP(-3) 0.084352 0.065527 1.287287 0.1986

IP(-4) -0.007017 0.071552 -0.098065 0.9219

IP(-5) -0.166242 0.047232 -3.519662 0.0005

FFR(-1) 0.044872 0.036526 1.228493 0.2199

FFR(-2) -0.037171 0.050673 -0.733540 0.4636

FFR(-3) -0.032724 0.055312 -0.591622 0.5544

FFR(-4) 0.037727 0.052131 0.723701 0.4696

FFR(-5) 0.013049 0.035630 0.366232 0.7144

PCEINFLATION(-1) 0.180072 0.085817 2.098311 0.0364

PCEINFLATION(-2) -0.314919 0.142431 -2.211022 0.0275

PCEINFLATION(-3) 0.101583 0.158060 0.642687 0.5207

PCEINFLATION(-4) -0.019244 0.157139 -0.122464 0.9026

PCEINFLATION(-5) 0.006674 0.093755 0.071181 0.9433

EBP(-1) -0.121419 0.053367 -2.275163 0.0233

EBP(-2) -0.154980 0.054988 -2.818403 0.0050

EBP(-3) -0.129754 0.054132 -2.396980 0.0169

EBP(-4) -0.045976 0.066354 -0.692891 0.4887

EBP(-5) -0.007993 0.065681 -0.121692 0.9032

UNEMP(-1) -0.252105 0.122004 -2.066363 0.0393

UNEMP(-2) -0.024110 0.154271 -0.156285 0.8759

UNEMP(-3) -0.120512 0.148132 -0.813548 0.4163

UNEMP(-4) 0.315541 0.157243 2.006708 0.0454

UNEMP(-5) 0.106194 0.131280 0.808910 0.4190

C 0.112507 0.180260 0.624140 0.5328

MA(1) 0.147980 2.012039 0.073547 0.9414

MA(2) 0.134471 2.536965 0.053005 0.9578

MA(3) 0.065694 2.774316 0.023679 0.9811

MA(4) 0.030319 3.187323 0.009512 0.9924

MA(5) 0.068029 1.720054 0.039551 0.9685

MA(6) 0.045049 4.041056 0.011148 0.9911

MA(7) 0.034612 2.344236 0.014765 0.9882

MA(8) 0.125890 2.544531 0.049475 0.9606

MA(9) 0.179498 2.715202 0.066109 0.9473

MA(10) 0.195885 2.713438 0.072191 0.9425

MA(11) 0.249114 1.867220 0.133415 0.8939

MA(12) -0.786232 2.823196 -0.278490 0.7808

SIGMASQ 0.203604 0.728346 0.279542 0.7800

R-squared 0.982097 Mean dependent var 1.441786






Prob(F-statistic) 0.000000

Inverted MA Roots .85+.45i .85-.45i .85 .51-.86i

.51+.86i -.00-1.00i -.00+1.00i -.49-.87i

-.49+.87i -.87+.50i -.87-.50i -1.00



7. ESTIMATE THE MODEL UP TO 2013M12. THEN, DO A DYNAMIC FORECAST, WITH

CONFIDENCE INTERVALS, FROM 2014M1 UP TO THE LATEST OBSERVATION IN THE SAMPLE.

COMMENT ON THE FITTED VALUES VS THE ACTUAL. NOTE: THE FITTED VALUES WON'T

NECESSARILY BE \GOOD," DON'T WORRY TOO MUCH ABOUT THAT. BUT IT'D BE GOOD IF YOU

CAN PROVIDE SOME EXPLANATION FOR THE BEHAVIOR OF THE FORECASTS BASED ON YOUR

KNOWLEDGE OF ARMA FORECASTING.

-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

The model fits the actual data pretty well for 2014, but in 2015 there is a big divergence between the two.

While the forecasted IPI aimed towards a stabilization in 2014 around the 3% range, the actual data shows that IPI declined steeply during this year.

What this data says is that the forecast wanted to go back to the momentum it had during the recovery from the last financial crisis, however, there have been several shocks to the American economy that have pushed IPI down such as the crash of oil prices, that delayed or cancelled many manufacturing projects related to the oil industry such as building wells, refineries, pipelines and the like.



1. ESTIMATE A VAR(12) FROM THE START OF THE SAMPLE UP TO 2013M12.

Vector Autoregression Estimates

Date: 08/02/16 Time: 21:10

Sample (adjusted): 1974M01 2013M12

Included observations: 480 after adjustments

Standard errors in ( ) & t-statistics in [ ]

IP UNEMP FFR EBP PCEINFLATION

IP(-1) 0.851393 -0.044540 0.040490 -0.031468 0.004500

(0.05057) (0.01322) (0.03269) (0.02038) (0.02897)

[ 16.8351] [-3.36958] [ 1.23855] [-1.54411] [ 0.15533]

IP(-2) 0.060732 0.022166 -0.002550 0.036315 0.094686

(0.06483) (0.01694) (0.04191) (0.02612) (0.03714)

[ 0.93684] [ 1.30819] [-0.06084] [ 1.39018] [ 2.54951]

IP(-3) 0.035230 -0.019469 -0.103080 0.000366 -0.051264

(0.06512) (0.01702) (0.04210) (0.02624) (0.03731)

[ 0.54099] [-1.14386] [-2.44868] [ 0.01395] [-1.37408]

IP(-4) 0.051243 0.028111 -0.053365 0.001081 -0.068647

(0.06580) (0.01720) (0.04253) (0.02651) (0.03770)

[ 0.77880] [ 1.63458] [-1.25465] [ 0.04075] [-1.82109]

IP(-5) -0.041405 0.008578 0.056458 -0.017309 -0.027652

(0.06622) (0.01731) (0.04281) (0.02668) (0.03794)

[-0.62529] [ 0.49565] [ 1.31896] [-0.64867] [-0.72892]

IP(-6) -0.119765 0.002692 0.011976 -0.002298 0.071720

(0.06627) (0.01732) (0.04284) (0.02671) (0.03797)

[-1.80720] [ 0.15539] [ 0.27954] [-0.08607] [ 1.88902]

IP(-7) -0.010616 0.025011 0.034650 -0.005396 0.004344

(0.06608) (0.01727) (0.04272) (0.02663) (0.03786)

[-0.16065] [ 1.44811] [ 0.81116] [-0.20266] [ 0.11474]

IP(-8) 0.011232 -0.021978 0.048107 -0.027821 0.018151

(0.06597) (0.01724) (0.04265) (0.02659) (0.03780)

[ 0.17025] [-1.27456] [ 1.12801] [-1.04647] [ 0.48023]

IP(-9) 0.063944 -0.022422 -0.020916 0.054467 -0.083133

(0.06591) (0.01723) (0.04260) (0.02656) (0.03776)

[ 0.97023] [-1.30164] [-0.49095] [ 2.05085] [-2.20177]



IP(-10) 0.034822 -0.003893 -0.061968 0.020144 0.036988

(0.06640) (0.01736) (0.04292) (0.02676) (0.03804)

[ 0.52441] [-0.22431] [-1.44367] [ 0.75283] [ 0.97231]

IP(-11) -0.031145 0.024663 -0.034609 -0.020389 -0.018554

(0.06572) (0.01718) (0.04248) (0.02648) (0.03765)

[-0.47390] [ 1.43578] [-0.81463] [-0.76989] [-0.49278]

IP(-12) -0.069127 -0.012722 0.037971 -0.015907 0.034440

(0.04781) (0.01250) (0.03091) (0.01927) (0.02739)

[-1.44583] [-1.01806] [ 1.22855] [-0.82562] [ 1.25733]

UNEMP(-1) -0.598125 0.918932 -0.693061 -0.033260 0.046232

(0.19721) (0.05155) (0.12748) (0.07947) (0.11298)

[-3.03292] [ 17.8276] [-5.43650] [-0.41853] [ 0.40920]

UNEMP(-2) 0.286472 0.093895 0.671587 0.147966 0.018104

(0.25885) (0.06766) (0.16733) (0.10431) (0.14829)

[ 1.10672] [ 1.38784] [ 4.01361] [ 1.41855] [ 0.12209]

UNEMP(-3) -0.260702 0.043898 -0.263159 -0.122576 -0.172910

(0.26515) (0.06930) (0.17140) (0.10685) (0.15190)

[-0.98324] [ 0.63343] [-1.53537] [-1.14723] [-1.13830]

UNEMP(-4) 0.472855 0.006869 0.054260 -0.110365 0.047042

(0.26579) (0.06947) (0.17181) (0.10710) (0.15227)

[ 1.77908] [ 0.09888] [ 0.31581] [-1.03046] [ 0.30894]

UNEMP(-5) -0.041823 0.003221 -0.073770 0.113528 -0.077982

(0.26597) (0.06952) (0.17193) (0.10718) (0.15237)

[-0.15725] [ 0.04633] [-0.42908] [ 1.05927] [-0.51179]

UNEMP(-6) -0.179830 -0.045788 0.515437 -0.009545 0.234649

(0.26409) (0.06903) (0.17071) (0.10642) (0.15130)

[-0.68095] [-0.66335] [ 3.01930] [-0.08969] [ 1.55093]

UNEMP(-7) 0.558519 -0.037256 -0.182075 -0.108196 0.088861

(0.26519) (0.06931) (0.17143) (0.10686) (0.15193)

[ 2.10608] [-0.53749] [-1.06210] [-1.01246] [ 0.58489]

UNEMP(-8) -0.073989 0.012878 -0.146226 0.093537 -0.202034

(0.26474) (0.06920) (0.17114) (0.10668) (0.15167)

[-0.27947] [ 0.18611] [-0.85443] [ 0.87678] [-1.33205]

UNEMP(-9) -0.293459 -0.038214 -0.087360 0.103114 0.067725

(0.26291) (0.06872) (0.16995) (0.10594) (0.15062)

[-1.11619] [-0.55609] [-0.51402] [ 0.97328] [ 0.44964]

UNEMP(-10) 0.565578 -0.013516 -0.018288 -0.021731 -0.050617

(0.26223) (0.06854) (0.16952) (0.10567) (0.15023)

[ 2.15677] [-0.19720] [-0.10788] [-0.20565] [-0.33692]

UNEMP(-11) -0.153923 0.130231 0.070839 -0.110795 -0.083607

(0.26034) (0.06804) (0.16829) (0.10491) (0.14915)

[-0.59125] [ 1.91391] [ 0.42094] [-1.05613] [-0.56057]



UNEMP(-12) -0.312412 -0.095599 0.123860 0.041358 0.086348

(0.19704) (0.05150) (0.12737) (0.07940) (0.11288)

[-1.58556] [-1.85631] [ 0.97245] [ 0.52089] [ 0.76495]

FFR(-1) 0.088422 -0.001493 1.318494 -0.030926 0.029397

(0.07829) (0.02046) (0.05061) (0.03155) (0.04485)

[ 1.12945] [-0.07296] [ 26.0535] [-0.98031] [ 0.65545]

FFR(-2) 0.013910 -0.021672 -0.585717 0.057440 0.075469

(0.12869) (0.03364) (0.08319) (0.05186) (0.07373)

[ 0.10809] [-0.64431] [-7.04078] [ 1.10764] [ 1.02363]

FFR(-3) -0.234409 0.055010 0.246952 -0.090196 -0.126679

(0.13578) (0.03549) (0.08777) (0.05472) (0.07779)

[-1.72638] [ 1.55005] [ 2.81355] [-1.64847] [-1.62851]

FFR(-4) 0.043279 -0.032452 -0.108431 0.061046 0.096011

(0.13869) (0.03625) (0.08966) (0.05589) (0.07946)

[ 0.31205] [-0.89521] [-1.20941] [ 1.09227] [ 1.20833]

FFR(-5) 0.023618 0.024341 0.266295 -0.001805 -0.108299

(0.13904) (0.03634) (0.08988) (0.05603) (0.07966)

[ 0.16986] [ 0.66977] [ 2.96272] [-0.03222] [-1.35955]

FFR(-6) 0.183743 -0.036458 -0.406481 -0.018628 0.121207

(0.13832) (0.03615) (0.08942) (0.05574) (0.07924)

[ 1.32838] [-1.00842] [-4.54599] [-0.33420] [ 1.52954]

FFR(-7) -0.073072 0.026365 0.182253 -0.015174 -0.145740

(0.13585) (0.03551) (0.08782) (0.05474) (0.07783)

[-0.53787] [ 0.74252] [ 2.07533] [-0.27718] [-1.87255]

FFR(-8) 0.030783 -0.031094 0.079722 0.078025 0.245225

(0.13235) (0.03459) (0.08556) (0.05333) (0.07583)

[ 0.23258] [-0.89884] [ 0.93179] [ 1.46294] [ 3.23408]

FFR(-9) 0.054236 0.034269 0.059074 -0.079237 -0.214497

(0.13266) (0.03467) (0.08576) (0.05346) (0.07600)

[ 0.40883] [ 0.98832] [ 0.68886] [-1.48222] [-2.82230]

FFR(-10) -0.139419 -0.000365 -0.146021 0.052756 0.181223

(0.13117) (0.03428) (0.08479) (0.05286) (0.07514)

[-1.06292] [-0.01066] [-1.72217] [ 0.99813] [ 2.41167]

FFR(-11) -0.102025 0.007592 0.090381 -0.061406 -0.200825

(0.12128) (0.03170) (0.07840) (0.04887) (0.06948)

[-0.84121] [ 0.23951] [ 1.15281] [-1.25643] [-2.89028]

FFR(-12) 0.141403 -0.024211 -0.016346 0.053652 0.055412

(0.07245) (0.01894) (0.04683) (0.02920) (0.04151)

[ 1.95169] [-1.27853] [-0.34900] [ 1.83766] [ 1.33499]

EBP(-1) -0.284737 0.021877 0.096712 0.618518 -0.154135

(0.12126) (0.03169) (0.07839) (0.04886) (0.06947)

[-2.34816] [ 0.69028] [ 1.23380] [ 12.6580] [-2.21876]

EBP(-2) -0.237933 0.022770 -0.208478 0.276333 0.084403



(0.14267) (0.03729) (0.09222) (0.05749) (0.08173)

[-1.66776] [ 0.61064] [-2.26057] [ 4.80665] [ 1.03267]

EBP(-3) -0.144058 -0.026394 0.159302 0.042714 0.095309

(0.14738) (0.03852) (0.09527) (0.05939) (0.08443)

[-0.97744] [-0.68519] [ 1.67207] [ 0.71921] [ 1.12879]

EBP(-4) 0.058897 0.037660 -0.088509 0.086876 -0.038061

(0.14738) (0.03852) (0.09527) (0.05939) (0.08443)

[ 0.39963] [ 0.97765] [-0.92902] [ 1.46283] [-0.45078]

EBP(-5) -0.042054 0.035788 -0.268393 -0.127089 -0.044290

(0.14732) (0.03851) (0.09523) (0.05937) (0.08440)

[-0.28546] [ 0.92940] [-2.81823] [-2.14073] [-0.52476]

EBP(-6) 0.034258 0.015063 0.226434 0.042509 0.030936

(0.14901) (0.03895) (0.09633) (0.06005) (0.08537)

[ 0.22990] [ 0.38676] [ 2.35068] [ 0.70792] [ 0.36238]

EBP(-7) 0.144006 -0.040832 -0.025906 -0.096827 0.038252

(0.14942) (0.03905) (0.09659) (0.06021) (0.08560)

[ 0.96376] [-1.04552] [-0.26821] [-1.60810] [ 0.44685]

EBP(-8) -0.111826 -0.003604 0.073836 -0.055785 -0.002022

(0.14920) (0.03900) (0.09644) (0.06012) (0.08547)

[-0.74952] [-0.09242] [ 0.76558] [-0.92787] [-0.02365]

EBP(-9) -0.118310 -0.049560 0.080355 0.022489 -0.011884

(0.14867) (0.03886) (0.09611) (0.05991) (0.08517)

[-0.79578] [-1.27539] [ 0.83612] [ 0.37539] [-0.13952]

EBP(-10) -0.030263 0.007163 -0.162486 -0.031050 0.035931

(0.14828) (0.03876) (0.09586) (0.05975) (0.08495)

[-0.20408] [ 0.18481] [-1.69512] [-0.51964] [ 0.42296]

EBP(-11) 0.188911 0.071567 -0.027153 0.080050 -0.045516

(0.14449) (0.03777) (0.09340) (0.05822) (0.08278)

[ 1.30745] [ 1.89505] [-0.29071] [ 1.37486] [-0.54986]

EBP(-12) -0.040634 -0.034595 -0.018233 0.000132 0.054917

(0.12920) (0.03377) (0.08352) (0.05206) (0.07402)

[-0.31450] [-1.02443] [-0.21831] [ 0.00254] [ 0.74193]

PCEINFLATION(-1) 0.172466 0.009833 0.077708 0.006539 1.372125

(0.08503) (0.02222) (0.05496) (0.03426) (0.04871)

[ 2.02837] [ 0.44245] [ 1.41379] [ 0.19085] [ 28.1682]

PCEINFLATION(-2) -0.293351 0.033352 -0.124313 0.027653 -0.457107

(0.14298) (0.03737) (0.09242) (0.05761) (0.08191)

[-2.05175] [ 0.89248] [-1.34504] [ 0.47996] [-5.58056]

PCEINFLATION(-3) 0.179532 -0.082357 0.112884 -0.034881 0.015379

(0.14772) (0.03861) (0.09549) (0.05953) (0.08463)

[ 1.21531] [-2.13299] [ 1.18211] [-0.58596] [ 0.18172]

PCEINFLATION(-4) -0.078973 0.121111 -0.196572 -0.008432 0.132875

(0.14562) (0.03806) (0.09413) (0.05868) (0.08342)



[-0.54233] [ 3.18209] [-2.08829] [-0.14369] [ 1.59278]

PCEINFLATION(-5) -0.048402 -0.128904 0.286528 0.079450 -0.153009

(0.14293) (0.03736) (0.09239) (0.05759) (0.08188)

[-0.33865] [-3.45061] [ 3.10123] [ 1.37946] [-1.86865]

PCEINFLATION(-6) -0.010267 0.090114 -0.257716 -0.054016 0.102585

(0.14358) (0.03753) (0.09281) (0.05786) (0.08225)

[-0.07151] [ 2.40133] [-2.77676] [-0.93362] [ 1.24716]

PCEINFLATION(-7) 0.163069 -0.030910 0.299275 -0.069599 0.057099

(0.14443) (0.03775) (0.09337) (0.05820) (0.08275)

[ 1.12903] [-0.81880] [ 3.20541] [-1.19583] [ 0.69005]

PCEINFLATION(-8) -0.152756 -0.013118 -0.151375 0.123073 -0.153506

(0.14576) (0.03810) (0.09422) (0.05874) (0.08351)

[-1.04800] [-0.34433] [-1.60656] [ 2.09534] [-1.83827]

PCEINFLATION(-9) 0.065207 -0.014182 -0.016128 -0.085528 0.152079

(0.14646) (0.03828) (0.09468) (0.05902) (0.08391)

[ 0.44523] [-0.37048] [-0.17035] [-1.44918] [ 1.81249]

PCEINFLATION(-10) -0.312193 0.033804 -0.065411 0.017477 0.032650

(0.14637) (0.03826) (0.09462) (0.05898) (0.08385)

[-2.13292] [ 0.88361] [-0.69133] [ 0.29630] [ 0.38936]

PCEINFLATION(-11) 0.279984 -0.034635 0.139895 -0.005028 -0.162414

(0.14075) (0.03679) (0.09098) (0.05672) (0.08063)

[ 1.98924] [-0.94148] [ 1.53757] [-0.08865] [-2.01420]

PCEINFLATION(-12) -0.004658 0.022750 -0.074462 0.005815 0.038126

(0.08382) (0.02191) (0.05418) (0.03378) (0.04802)

[-0.05557] [ 1.03842] [-1.37425] [ 0.17215] [ 0.79395]

C 0.477025 0.124342 0.218264 0.087025 0.018364

(0.17635) (0.04609) (0.11400) (0.07106) (0.10103)

[ 2.70504] [ 2.69769] [ 1.91467] [ 1.22463] [ 0.18177]

R-squared 0.972998 0.991346 0.988547 0.813500 0.988997

Adj. R-squared 0.969132 0.990107 0.986907 0.786793 0.987421

Sum sq. resids 153.1446 10.46209 63.99462 24.86804 50.26377

S.E. equation 0.604566 0.158016 0.390809 0.243620 0.346354

F-statistic 251.6433 799.9726 602.7531 30.46074 627.6738

Log likelihood -406.9137 237.1562 -197.4936 29.35810 -139.5301

Akaike AIC 1.949640 -0.733984 1.077057 0.131841 0.835542

Schwarz SC 2.480059 -0.203566 1.607475 0.662260 1.365961

Mean dependent 1.376945 6.513542 5.127667 0.051699 4.274951

S.D. dependent 3.441029 1.588675 3.415417 0.527610 3.088147

Determinant resid covariance (dof adj.) 8.39E-06

Determinant resid covariance 4.25E-06

Log likelihood -437.0429

Akaike information criterion 3.091845

Schwarz criterion 5.743939



2. DO IMPULSE RESPONSE FUNCTIONS USING THE CHOLESKY DECOMPOSITION, FOR 60 LAGS.

ORDER THIS WAY: UNEMPLOYMENT RATE, PCE INFLATION, INDUSTRIAL PRODUCTION, EXCESS

BOND PREMIUM, THE 3-MONTH RATE.

-1.2

-0.8

-0.4

0.0

0.4

0.8

5 10 15 20 25 30 35 40 45 50 55 60

Response of IP to UNEMP

-1.2

-0.8

-0.4

0.0

0.4

0.8

5 10 15 20 25 30 35 40 45 50 55 60

Response of IP to PCEINFLATION

-1.2

-0.8

-0.4

0.0

0.4

0.8

5 10 15 20 25 30 35 40 45 50 55 60

Response of IP to IP

-1.2

-0.8

-0.4

0.0

0.4

0.8

5 10 15 20 25 30 35 40 45 50 55 60

Response of IP to EBP

-1.2

-0.8

-0.4

0.0

0.4

0.8

5 10 15 20 25 30 35 40 45 50 55 60

Response of IP to FFR

Response to Cholesky One S.D. Innovations ± 2 S.E.



3) EXPLAIN WHAT THE ORDERING IMPLIES REGARDING THE CORRELATION OF SAME-PERIOD

INNOVATIONS TO EACH OF THE VARIABLES.

Because the Cholesky decomposition method imposes a recursive structure on the variables, the

contemporary relationships of the variables is going to be affected by their ordering.

In this case, the first variable is unemployment rate, which means it is going to be affected by its

current innovation only and not by any of the subsequent variables’ current innovations.

Innovations to the second variable, pce inflation, will be affected by its current innovations, plus

those of the preceding unemployment rate variable. Innovations to the third variable, industrial

production, will be affected by its current innovations plus the current innovations of the preceding

two variables.

This pattern will continue all the way through to the last variable ordered. Therefore, the recursive

nature of Cholesky decomposition means the variable that is ordered first is going to have effects on

all the subsequent variables.

Thus, it makes sense to order the variables from most exogenous to least exogenous. In contrast, the

residual method sets the impulses to one standard deviation of the residuals, which ignores the

correlations in the VAR residuals. Therefore, when using the residual method, the order of the

impulse variables is not going to matter.

4) PLOT THE RESPONSE OF THE UNEMPLOYMENT RATE TO STANDARDIZED SHOCKS TO THE 5

VARIABLES.



The only shock that will affect the unemployment rate in the same period is a shock to itself - the

unemployment rate.

A shock to pceinflation will start to significantly affect the unemployment rate a few months after the

initial shock. Peak effects of the shock are felt after 30 months after which they slowly start to wear

off. This suggests that the unemployment rate will feel effects from a shock in pceinflation for at least

5 after the fact.

A shock to ip will be felt by unemp soon after the initial shock. In this case, unemployment rate will

actually go down until about the 15th month when it will start trending back to its pre-shock level.

Unemp responds to a shock in ebp by rising sharply soon after the initial shock, peaking after about 17

months. The effects from the shock then begin to decrease, finally arrive back at zero between 50-55

months after the initial shock.

Ffr is the last impulse variable in this Cholesky impulse response function, which means it’s going to

include innovations from all the previous variables as well. A shock to the ffr will slowly start to

impact the unemployment rate after about 1 year. The effect will continue slowly climbing then start

to level off after about 35 months.



5) THE UNEMPLOYMENT RATE TENDS TO GO UP WHEN THE EBP GOES UP. HOW DOES THE EBP

AFFECT OTHER VARIABLES? PLOT THE IRF OF EACH OF THE 5 VARIABLES TO A STANDARDIZED

SHOCK TO THE EBP.

-.2

-.1

.0

.1

.2

.3

5 10 15 20 25 30 35 40 45 50 55 60

Response of UNEMP to EBP

-.6

-.4

-.2

.0

.2

.4

5 10 15 20 25 30 35 40 45 50 55 60

Response of PCEINFLATION to EBP

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

5 10 15 20 25 30 35 40 45 50 55 60

Response of IP to EBP

-.1

.0

.1

.2

.3

5 10 15 20 25 30 35 40 45 50 55 60

Response of EBP to EBP

-.5

-.4

-.3

-.2

-.1

.0

.1

.2

5 10 15 20 25 30 35 40 45 50 55 60

Response of FFR to EBP

Response to Cholesky One S.D. Innovations ± 2 S.E.



Explanation:

When you look at the effect that EBP has on unemp, pceinflation, IP, and FFR you can see that the initial shock on these 4 variables is zero.

When you look at the response of the unemployment rate to a shock in EBP, a change of EBP

today has a peak effect on unemp around the 20th month of about .18. This illustrates how when credit conditions tighten, unemployment rate goes up. After this, the effects of the initial EBP’s shock start to wear off and unemp has a gradual decrease back towards zero, and finally reaches zero around the 52nd month.

When credit conditions tighten, pceinflation will not immediately respond in that same period, but shortly after pceinflation begins to drop and reaches a negative-peak effect around the 16th month of about -.2. It takes about 55 months for inflation to return to pre-shock levels.

A shock on EBP today leads to a subsequent negative response by IP that continues to decline until about the 10th month where it hits a negative peak effect of -.75. At this point, IP begins to rise back up until it reaches a positive peak effect on the 32nd month of about .22. After the 32nd month the effect of the ebp shock on ip stabilizes as it drifts closer towards zero.

The response of FFR due to a shock to EBP has a small but positive peak effect of about .015 during the first month (which may or may not be statistically significant) and then drops to a negative peak effect of about -.25 in the 17th month. Subsequently the effect on FFR remains negative however it gradually drifts back towards zero.

Additionally the effect of EBP on EBP has a positive initial effect of about .24, and then later decreases towards zero by the 25th month. In the periods after the initial EBP shock, EBP drops to negative figures, and remain fairly constant around -.02.



6) LASTLY, SOLVE THE MODEL UP TO 2019 M12. FORECAST THE UNEMPLOYMENT RATE,

INCLUDING CONFIDENCE INTERVALS.

2

3

4

5

6

7

8

9

10

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019

unemp unemp (Baseline Mean)

U_LB U_UB

The forecasted unemployment rate is pretty similar to that of the actual unemployment rate until about the middle of 2014. At this time, the actual path of the unemployment rate continues its downward trend while the forecasted unemployment rate starts declining at a slower rate until the end of 2015 when we see the forecast starts to go back up as it heads back towards the mean.

7) REFERENCES

1, Investopedia. "Industrial Production and Capacity Utilization - G.17." Industrial Production and

Capacity Utilization. Investopedia, 2016. Web. 08 Aug. 2016.

2, The Federal Reserve. "Industrial Production and Capacity Utilization - G.17."Industrial Production

and Capacity Utilization. The Federal Reserve, 1 Apr. 2016. Web. 08 Aug. 2016.

arma and var modelling of industrial production in america

Economy & Finance