Global Analysts Eirik Skeid, Anders Graham, Bradley Moore, Matthew Scott Tor Seim, Steven Comstock

Global Analysts

Eirik Skeid, Anders Graham,

Bradley Moore, Matthew Scott Tor Seim, Steven Comstock

Project Purpose

Investigate the correlation between USA’s unemployment and inflation rates.

Construct a model which can be used for approximate inflation forecasting.

Outline

Characterize the data Test for Unit Roots Pre-Whitten the time series Investigate Causality Bivariate Model Construction Remodel Forecast and Evaluate Results

DataTraces

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INFLATION

Inflation Calculation based on:

CPI-CPI(-12) / CPI(-12).

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UNEM

Unemployment Trace

Histograms

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Series : INFLATIONSample 1949:01 2007:03Observations 699

Mean 0.037713Median 0.030880Max imum 0.147560Minimum -0.028690Std. Dev. 0.030048Skewness 1.283760Kurtos is 4.836957

Jarque-Bera 290.2763Probability 0.000000

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Series : UNEMSample 1949:01 2007:04Observations 700

Mean 5.635000Median 5.600000Max imum 10.80000Minimum 2.500000Std. Dev. 1.500707Skewness 0.567713Kurtos is 3.516460

Jarque-Bera 45.38114Probability 0.000000

Inflation:•Multi-peaked•Positively Skewed•Slightly Kurtotic•Not Normal

Unemployment:•Multi-peaked•Not Normal

CorrelogramsInflation UnemploymentBoth appear to be random walks and require unit root test.

Unit Roots Tests

ADF Test Statistic -2.793594 1% Critical Value*

-3.4424

5% Critical Value

-2.8661

10% Critical Value

-2.5692

Inflation Unemployment

ADF Test Statistic -1.916942 1% Critical Value*

-3.4422

5% Critical Value

-2.8660

10% Critical Value

-2.5692

Both are evolutionary.

Differencing

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DINFLATION

Inflation Unemployment

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DUNEM

Differenced Histograms

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Series : DINFLATIONSample 1949:02 2007:03Observations 698

Mean 0.002168Median -0.002000Max imum 2.153000Minimum -2.039000Std. Dev. 0.424951Skewness 0.124286Kurtos is 7.772432

Jarque-Bera 664.2021Probability 0.000000

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Series : DUNEMSample 1949:02 2007:04Observations 699

Mean 0.000286Median 0.000000Max imum 1.300000Minimum -1.500000Std. Dev. 0.214115Skewness 0.340677Kurtos is 9.419683

Jarque-Bera 1213.830Probability 0.000000

Inflation:•Kurtotic•Not Normal

Unemployment:•Kurtotic•Not normal

Differenced Inflation Correlogram

Looks like a seasonal ARMA(2,2).

The reason for the spike at 12 is because of the definition of inflation CPI-CPI(-12) / CPI(-12).

It does not look over differenced.

Unemployment Correlogram

Granger Causality Test

Pairwise Granger Causality Tests Date: 05/31/07 Time: 19:51 Sample: 1949:01 2007:04 Lags: 12

Null Hypothesis: Obs F-Statistic Probability

DUNEM does not Granger Cause DINFLATION 686 4.17866 2.4E-06 DINFLATION does not Granger Cause DUNEM 0.47418 0.93005

Results show one way causality, unemployment affects inflation

Cross Correlations

VAR Impulse Response

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Response of DINFLATION to DINFLATION

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Response of DINFLATION to DUNEM

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Response of DUNEM to DINFLATION

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Response of DUNEM to DUNEM

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

VAR Impulse Response

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Response of DINFLATION to DINFLATION

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Response of DINFLATION to DUNEM

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Response of DUNEM to DINFLATION

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Response of DUNEM to DUNEM

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

Inflation Model

Dependent Variable: DINF Method: ML - ARCH Date: 06/01/07 Time: 10:45 Sample(adjusted): 1951:10 2007:03 Included observations: 666 after adjusting endpoints Convergence achieved after 23 iterations Backcast: 1950:10 1951:09

Coefficient Std. Error z-Statistic Prob.

DUNEM(-8) -0.095073 0.038123 -2.493818 0.0126 AR(1) 0.208462 0.042508 4.904030 0.0000 AR(2) 0.187172 0.039713 4.713126 0.0000 AR(7) 0.123481 0.037743 3.271624 0.0011 AR(9) 0.085019 0.039976 2.126754 0.0334 AR(10) 0.118897 0.038506 3.087717 0.0020 AR(12) -0.113026 0.038087 -2.967558 0.0030 AR(15) 0.110151 0.036492 3.018500 0.0025 AR(24) -0.146959 0.032104 -4.577601 0.0000 MA(11) 0.104528 0.019561 5.343553 0.0000 MA(12) -0.782336 0.019995 -39.12726 0.0000

Variance Equation

C 0.003712 0.001110 3.343397 0.0008 ARCH(1) 0.151702 0.028644 5.296180 0.0000

GARCH(1) 0.802292 0.034546 23.22355 0.0000

R-squared 0.530402 Mean dependent var -0.006288 Adjusted R-squared 0.521039 S.D. dependent var 0.375694 S.E. of regression 0.260006 Akaike info criterion 0.073361 Sum squared resid 44.07740 Schwarz criterion 0.167983 Log likelihood -10.42924 F-statistic 56.64776 Durbin-Watson stat 1.938664 Prob(F-statistic) 0.000000

Inverted AR Roots .95 -.08i .95+.08i .86+.35i .86 -.35i .74+.58i .74 -.58i .60+.70i .60 -.70i .34 -.86i .34+.86i .15 -.89i .15+.89i -.13+.92i -.13 -.92i -.34+.85i -.34 -.85i -.54 -.72i -.54+.72i -.75+.56i -.75 -.56i -.85+.34i -.85 -.34i -.91 -.15i -.91+.15i

Inverted MA Roots .97 .84+.48i .84 -.48i .50 -.84i .50+.84i .01 -.98i .01+.98i -.49 -.86i -.49+.86i -.85+.50i -.85 -.50i -.99

ResidualsCorrelograms of the residuals and the squared residuals.

Forecasting of Inflation

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INFFINFFL

INFFUINF

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INF07UINF07L

INF07INF

Tracking Plot Forecast

Model Improvement

Removing imputed structure in CPI calculation.

Old Equation: CPI-CPI(-12) / CPI(-12)

New Equation: CPI-CPI(-1) / CPI(-1)

Data Identification

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INFLATION2

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Series: INFLATION2Sample 1949:02 2007:04Observations 699

Mean 3.709728Median 3.582090Maximum 21.67043Minimum -10.08403Std. Dev. 4.293659Skewness 0.410974Kurtosis 4.386076

Jarque-Bera 75.63192Probability 0.000000

Trace Histogram

Unit Root Test for CPI Data

ADF Test Statistic -3.431205 1% Critical Value*

-3.4424

5% Critical Value

-2.8661

10% Critical Value

-2.5692

Differenced CPI Data

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DIN

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Series: DINSample 1949:03 2007:04Observations 698

Mean 0.025495Median -0.005849Maximum 18.95550Minimum -19.00968Std. Dev. 4.279287Skewness -0.162033Kurtosis 4.915232

Jarque-Bera 109.7353Probability 0.000000

Stationary, yet not normal.

Granger causality test

Pairwise Granger Causality Tests Date: 06/01/07 Time: 11:46 Sample: 1949:04 2007:04 Lags: 12

Null Hypothesis: Obs F-Statistic Probability

DUNEM does not Granger Cause DIN 685 2.78029 0.00104 DIN does not Granger Cause DUNEM 0.45937 0.93785

Unemployment seems to cause inflation but not the opposite

Estimation Output for Best Model

Dependent Variable: DIN Method: ML - ARCH Date: 06/01/07 Time: 10:20 Sample(adjusted): 1952:05 2006:04 Included observations: 648 after adjusting endpoints Convergence achieved after 41 iterations Backcast: 1952:02 1952:04

Coefficient Std. Error z-Statistic Prob.

C 0.000943 0.014862 0.063476 0.9494 DUNEM(-3) -0.909459 0.181043 -5.023453 0.0000

AR(11) 0.081456 0.038564 2.112251 0.0347 AR(12) 0.191082 0.040177 4.756017 0.0000 AR(34) -0.134611 0.032547 -4.135958 0.0000 AR(36) 0.199666 0.031593 6.319992 0.0000 MA(1) -0.802523 0.031746 -25.27981 0.0000 MA(3) -0.108571 0.030626 -3.545056 0.0004

Variance Equation

C 0.578962 0.249201 2.323276 0.0202 ARCH(1) 0.125292 0.022222 5.638220 0.0000 ARCH(2) 0.074787 0.027533 2.716271 0.0066

GARCH(1) -0.111933 0.033232 -3.368218 0.0008 GARCH(2) 0.857783 0.031214 27.48052 0.0000

R-squared 0.431494 Mean dependent var 0.008715 Adjusted R-squared 0.420750 S.D. dependent var 3.957843 S.E. of regression 3.012254 Akaike info criterion 4.961863 Sum squared resid 5761.783 Schwarz criterion 5.051617 Log likelihood -1594.644 F-statistic 40.16349 Durbin-Watson stat 1.966808 Prob(F-statistic) 0.000000

Inverted AR Roots .95 .92+.14i .92 -.14i .88+.31i .88 -.31i .84+.47i .84 -.47i .75+.59i .75 -.59i .62+.73i .62 -.73i .49 -.84i .49+.84i .35+.90i .35 -.90i .17 -.95i .17+.95i -.00 -.98i -.00+.98i -.16 -.95i -.16+.95i -.34 -.90i -.34+.90i -.50+.84i -.50 -.84i -.62 -.73i -.62+.73i -.74 -.60i -.74+.60i -.84 -.46i -.84+.46i -.89+.31i -.89 -.31i -.92 -.15i -.92+.15i -.94

Inverted MA Roots .93 -.06+.34i -.06 -.34i

Forecasting

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D IN FTEST ± 2 S.E.

Forecast: DINFTESTActual: DINSample: 2006:05 2007:04Include observations: 12

Root Mean Squared Error 4.460440Mean Absolute Error 3.774718Mean Abs. Percent Error 160.3528Theil Inequality Coefficient 0.647216 Bias Proportion 0.001770 Variance Proportion 0.035402 Covariance Proportion 0.962828

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Forec as t of Var ianc e

Recolored Forecast

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INFEINFLATIONF

INFLATIONF+2*SEF2INFLATIONF-2*SEF2

Date Inflation Forecast

2007:05:00 6.41 2007:06:00 4.25 2007:07:00 2.60 2007:08:00 1.59 2007:09:00 1.03 2007:10:00 2.66 2007:11:00 1.69 2007:12:00 0.81

Conclusion The best model uses the CPI based on monthly

changes instead of annual. The coefficient on dunem is negative. So an

increase in unemployment rate will result in a decrease in inflation, all else held constant.

This is correct according to macroeconomic theory. Inflation and unemployment rate are inversely related probably with a small lag, in our case 3 months.

The inclusion of additional correlated variables could increase forecasting accuracy