Economics 240CEconomics 240C

Forecasting US Retail Forecasting US Retail SalesSales

Group 3Group 3

Simon RosenSimon Rosen Michael Jelmini Kenneth Morino Sylvia Salinas Yuan Yuan Ray Zuo Erding Luo

Motivations:Motivations:

Forecasting US retail sales for the Forecasting US retail sales for the remaining months of 2004 to remaining months of 2004 to provide indicative evidence to provide indicative evidence to explore George W. Bush’s claim of explore George W. Bush’s claim of economic recovery. economic recovery.

Introduction:Introduction:

Retail Sales as an economic Retail Sales as an economic indicator:indicator:

Consumer ConfidenceConsumer Confidence

General Economic PerformanceGeneral Economic Performance

Business Cycle ‘Turns’Business Cycle ‘Turns’

Data:Data:

Real Retail and Food Service data Real Retail and Food Service data obtained from Fred IIobtained from Fred II

Monthly Time Series from January Monthly Time Series from January 1992 to April 2004.1992 to April 2004.

Seasonally AdjustedSeasonally Adjusted

Initial Observations:Initial Observations:

Evolutionary Evolutionary SeriesSeries

Trend in meanTrend in mean

Unit Root Test :Unit Root Test :

120000

130000

140000

150000

160000

170000

180000

92 93 94 95 96 97 98 99 00 01 02 03 04

SALES

ADF Test Statistic -0.09305310% Critical Value -2.6745

0

5

10

15

20

25

12000013000014000015000016000 1070000180000

Series: SALESSample 1992:01 2004:04Observations 148

Mean 148619.1Median 146538.5Maximum 178098.0Minimum 120607.0Std. Dev. 16095.97Skewness -0.097460Kurtosis 1.767251

Jarque-Bera 9.605597Probability 0.008207

StationarityStationarity Difference Data into fractional change to Difference Data into fractional change to

achieve stationarity: Dsales = Sales – achieve stationarity: Dsales = Sales – Sales(-1)Sales(-1)

-10000

-5000

0

5000

10000

15000

92 93 94 95 96 97 98 99 00 01 02 03 04

DSALES

0

10

20

30

40

-5000-2500 0 2500 5000 7500 10000

Series: DSALESSample 1992:02 2004:04Observations 147

Mean 376.5374Median 368.0000Maximum 10945.00Minimum -5031.000Std. Dev. 1473.569Skewness 1.920182

Kurtosis 20.60472

Jarque-Bera 1988.632Probability 0.000000

Correlogram and Root TestCorrelogram and Root Test

September 11thSeptember 11th

Large Spike in Large Spike in series between series between September and September and October 2001October 2001

Intervention Intervention Model needed for Model needed for this one off event.this one off event.

-10000

-5000

0

5000

10000

15000

92 93 94 95 96 97 98 99 00 01 02 03 04

DSALES

After achieving an approximately stationary series:

Intervention modelIntervention model We use time We use time

dummies to model dummies to model the pulse function for the pulse function for the September 11the September 11thth 2001 event. We put 2001 event. We put in dummies for the in dummies for the months of months of September, October, September, October, November of 2001.November of 2001.

So our model So our model becomes an becomes an intervention model.intervention model.

1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

East

North

Date Dsales Step Variable1/1/2001 933 02/1/2001 -195 03/1/2001 -1223 04/1/2001 1842 05/1/2001 45 06/1/2001 -1050 07/1/2001 -329 08/1/2001 627 09/1/2001 -3260 -0.3

10/1/2001 10945 111/1/2001 -5031 -0.512/1/2001 -683 01/1/2002 -768 02/1/2002 906 03/1/2002 -722 04/1/2002 1554 05/1/2002 -2140 06/1/2002 1494 07/1/2002 1088 08/1/2002 173 09/1/2002 -2369 0

10/1/2002 674 011/1/2002 632 012/1/2002 1467 0

Model Estimation IModel Estimation I

Model I ResidualsModel I Residuals

0

5

10

15

20

-2000 -1000 0 1000 2000

Series: ResidualsSample 1992:09 2004:04Observations 140

Mean -15.26165Median 48.56197Maximum 2377.545Minimum -2676.280Std. Dev. 897.8525Skewness -0.405495Kurtosis 3.428258

Jarque-Bera 4.906470Probability 0.086015

Model Estimation IIModel Estimation II

Model II Residual Model II Residual Comparing the residuals of model II with those of Comparing the residuals of model II with those of

model I, there is an improvement in the Jarque-Bera model I, there is an improvement in the Jarque-Bera statistic. This shows that the ARCH/GARCH improves statistic. This shows that the ARCH/GARCH improves the model. the model.

Diagnostic of the modelDiagnostic of the model

The actual-The actual-fitted residual fitted residual graph shows graph shows that the model that the model tracks the tracks the observations observations well, especially well, especially the large spike the large spike due to the due to the 9/11/2001 9/11/2001 event.event.

Note:Note:

The pulse function is highly significantThe pulse function is highly significant Equation as a whole highly significantEquation as a whole highly significant Variance Term Arch(1) included to Variance Term Arch(1) included to

improve Kurtosis of model’s residualsimprove Kurtosis of model’s residuals Lack of structure or significant spikes Lack of structure or significant spikes

in residual correlogramin residual correlogram

Forecast of dsales for Forecast of dsales for 2004:05 2004:05 to 2004:12to 2004:12

-8000

-4000

0

4000

8000

12000

1992 1994 1996 1998 2000 2002 2004

DSALESDSALESF

DSALESF+2*SEFDSALESF-2*SEF

Forecast of retail salesForecast of retail sales

120000

130000

140000

150000

160000

170000

180000

190000

1992 1994 1996 1998 2000 2002 2004

SALESF SALES

ConclusionConclusion Our forecast shows the Our forecast shows the

difference in retail sales difference in retail sales is not going to fluctuate is not going to fluctuate very much in the rest of very much in the rest of 2004. 2004.

The absolute value of The absolute value of retail sales will continue retail sales will continue its upward trend.its upward trend.

Whether it signals Whether it signals economic recovery is economic recovery is rather unclear and it will rather unclear and it will make President Bush make President Bush reelection campaign less reelection campaign less certain too.certain too.