Auto sales

• GROUP G (for Gr-r-reat!!!)– Salem Engler– Aidis Malinauskas– Elizabeth Mallon– Peachie Maher– Robert Patrick II– Jared Smith

Introduction

• The goal of this project was to forecast auto sales based on ARMA and ARCH/GARCH modeling techniques.

• The data set used:– Light Weight Vehicle Sales: Autos and Light

Trucks

• Auto sales can be used an economic indicator

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00:01 00:07 01:01 01:07 02:01 02:07 03:01

AUTOSALES

8

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12

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76 78 80 82 84 86 88 90 92 94 96 98 00 02

AUTOSALES

2.0

2.2

2.4

2.6

2.8

3.0

3.2

76 78 80 82 84 86 88 90 92 94 96 98 00 02

LOGAUTOSALES

-0.4

-0.2

0.0

0.2

0.4

76 78 80 82 84 86 88 90 92 94 96 98 00 02

DLNAUTO

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80

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2

Series: DLNAUTOSample 1976:02 2003:04Observations 327

Mean 0.000821Median 0.001954Maximum 0.274187Minimum -0.380745Std. Dev. 0.070595Skewness -0.853777Kurtosis 9.470532

Jarque-Bera 610.1755Probability 0.000000

ADF Test Statistic -9.906274 1% Critical Value* -3.4526 5% Critical Value -2.8707 10% Critical Value -2.5716

*MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey-Fuller Test Equation Dependent Variable: D(DLNAUTO)

Method: Least Squares Date: 05/27/03 Time: 19:06

Sample(adjusted): 1976:08 2003:04 Included observations: 321 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob.

DLNAUTO(-1) -2.523592 0.254747 -9.906274 0.0000 D(DLNAUTO(-1)) 1.062135 0.227710 4.664428 0.0000 D(DLNAUTO(-2)) 0.600626 0.191177 3.141731 0.0018 D(DLNAUTO(-3)) 0.279517 0.147101 1.900175 0.0583 D(DLNAUTO(-4)) 0.088766 0.100540 0.882892 0.3780 D(DLNAUTO(-5)) -0.010015 0.056926 -0.175921 0.8605

C 0.001772 0.003541 0.500553 0.6170

R-squared 0.693573 Mean dependent var -3.83E-05 Adjusted R-squared 0.687718 S.D. dependent var 0.113364 S.E. of regression 0.063350 Akaike info criterion -2.658714 Sum squared resid 1.260157 Schwarz criterion -2.576471

Log likelihood 433.7236 F-statistic 118.4525 Durbin-Watson stat 1.997111 Prob(F-statistic) 0.000000

Dependent Variable: DLNAUTO Method: Least Squares

Date: 05/27/03 Time: 19:11 Sample(adjusted): 1976:07 2003:04

Included observations: 322 after adjusting endpoints Convergence achieved after 3 iterations

Variable Coefficient Std. Error t-Statistic Prob.

C 0.000730 0.001381 0.528244 0.5977 AR(1) -0.462527 0.055961 -8.265162 0.0000 AR(2) -0.463762 0.060733 -7.636069 0.0000 AR(3) -0.324470 0.063573 -5.103897 0.0000 AR(4) -0.195214 0.061047 -3.197785 0.0015 AR(5) -0.102830 0.056433 -1.822167 0.0694

R-squared 0.222857 Mean dependent var 0.000779 Adjusted R-squared 0.210561 S.D. dependent var 0.071091 S.E. of regression 0.063165 Akaike info criterion -2.667680 Sum squared resid 1.260777 Schwarz criterion -2.597346

Log likelihood 435.4964 F-statistic 18.12354 Durbin-Watson stat 1.997452 Prob(F-statistic) 0.000000

Inverted AR Roots .32 -.62i .32+.62i -.26 -.55i -.26+.55i -.57

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80

-0.3 -0.2 -0.1 0.0 0.1 0.2

Series: ResidualsSample 1976:07 2003:04Observations 322

Mean -3.07E-15Median 0.002482Maximum 0.267327Minimum -0.359100Std. Dev. 0.062671Skewness -0.508669Kurtosis 8.804142

Jarque-Bera 465.8675Probability 0.000000

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0.02

0.04

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0.12

0.14

76 78 80 82 84 86 88 90 92 94 96 98 00 02

RESIDUALSSQ

ARCH Test:

F-statistic 16.62630 Probability 0.000058 Obs*R-squared 15.90174 Probability 0.000067

Test Equation:

Dependent Variable: RESID^2 Method: Least Squares

Date: 05/27/03 Time: 19:15 Sample(adjusted): 1976:08 2003:04

Included observations: 321 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob.

C 0.003052 0.000635 4.804844 0.0000 RESID^2(-1) 0.222582 0.054587 4.077536 0.0001

R-squared 0.049538 Mean dependent var 0.003926 Adjusted R-squared 0.046559 S.D. dependent var 0.010971 S.E. of regression 0.010712 Akaike info criterion -6.228656 Sum squared resid 0.036606 Schwarz criterion -6.205158

Log likelihood 1001.699 F-statistic 16.62630 Durbin-Watson stat 1.995072 Prob(F-statistic) 0.000058

Dependent Variable: DLNAUTO Method: ML - ARCH

Date: 05/27/03 Time: 19:19 Sample(adjusted): 1976:07 2003:04

Included observations: 322 after adjusting endpoints Convergence achieved after 39 iterations

Coefficient Std. Error z-Statistic Prob.

C 0.003312 0.000979 3.383796 0.0007 AR(1) -0.431238 0.067594 -6.379839 0.0000 AR(2) -0.420639 0.052031 -8.084441 0.0000 AR(3) -0.368715 0.052617 -7.007486 0.0000 AR(4) -0.196033 0.058470 -3.352731 0.0008 AR(5) -0.108699 0.049664 -2.188677 0.0286

Variance Equation

C 0.001327 0.000258 5.139963 0.0000 ARCH(1) 0.600328 0.128366 4.676696 0.0000

GARCH(1) 0.174044 0.092254 1.886577 0.0592

R-squared 0.208836 Mean dependent var 0.000779 Adjusted R-squared 0.188615 S.D. dependent var 0.071091 S.E. of regression 0.064037 Akaike info criterion -2.880705 Sum squared resid 1.283523 Schwarz criterion -2.775205

Log likelihood 472.7935 F-statistic 10.32747 Durbin-Watson stat 2.040887 Prob(F-statistic) 0.000000

Inverted AR Roots .34 -.65i .34+.65i -.24 -.52i -.24+.52i -.62

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-2.50 -1.25 0.00 1.25 2.50 3.75 5.00

Series: Standardized ResidualsSample 1976:07 2003:04Observations 322

Mean -0.053874Median -0.114321Maximum 5.389817Minimum -3.296816Std. Dev. 1.000014Skewness 0.557478Kurtosis 6.034521

Jarque-Bera 140.2235Probability 0.000000

Dependent Variable: DLNAUTO Method: ML - ARCH

Date: 05/27/03 Time: 18:48 Sample(adjusted): 1976:11 2003:04

Included observations: 318 after adjusting endpoints Convergence achieved after 24 iterations

Coefficient Std. Error z-Statistic Prob.

SQR(GARCH) -0.153498 0.078643 -1.951817 0.0510 C 0.012357 0.004691 2.634011 0.0084

AR(1) -0.420227 0.064909 -6.474086 0.0000 AR(2) -0.446118 0.053820 -8.289137 0.0000 AR(3) -0.396552 0.051773 -7.659445 0.0000 AR(4) -0.192549 0.056283 -3.421056 0.0006 AR(9) 0.120889 0.030931 3.908332 0.0001 AR(5) -0.102094 0.041621 -2.452947 0.0142

Variance Equation

C 0.001319 0.000224 5.884868 0.0000 ARCH(1) 0.649669 0.134643 4.825105 0.0000

GARCH(1) 0.130606 0.078112 1.672044 0.0945

R-squared 0.239701 Mean dependent var 0.000836 Adjusted R-squared 0.214935 S.D. dependent var 0.071369 S.E. of regression 0.063236 Akaike info criterion -2.909989 Sum squared resid 1.227629 Schwarz criterion -2.779855

Log likelihood 473.6883 F-statistic 9.678832 Durbin-Watson stat 2.141313 Prob(F-statistic) 0.000000

Inverted AR Roots .65 .50+.61i .50 -.61i .14+.82i .14 -.82i -.41 -.70i -.41+.70i -.77 -.25i -.77+.25i

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-3 -2 -1 0 1 2 3 4

Series: Standardized ResidualsSample 1976:11 2003:04Observations 318

Mean -0.307527Median -0.345449Maximum 4.385248Minimum -3.614494Std. Dev. 0.977273Skewness 0.359804Kurtosis 5.294955

Jarque-Bera 76.64667Probability 0.000000

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-0.1

0.0

0.1

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03:04 03:05 03:06 03:07 03:08 03:09 03:10 03:11 03:12

DLNAUTOF ± 2 S.E.

Forecast: DLNAUTOFActual: DLNAUTOSample: 2003:04 2003:12Include observations: 1

Root Mean Squared Error 0.039367Mean Absolute Error 0.039367Mean Abs. Percent Error 220.1094

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0.006

03:04 03:05 03:06 03:07 03:08 03:09 03:10 03:11 03:12

Forecast of Variance

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DLNAUTOFORECAST

UPPERLOWER

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95 96 97 98 99 00 01 02 03

AUTOF AUTOSALES

Closing

• Forecast is relatively flat around 16.5 million units

• “Speaking at NADA's 86th Annual Convention & Exposition in San Francisco, NADA Chief Economist Paul Taylor projected that new car and light truck sales of 16.5 million in 2003, down from 16.8 million in 2002.”