ECO 5375 701 Eco and Bus Forecasting Prof Tom Fomby Fall 2014 EXERCISE 4 Purpose To learn how to use the DTDS model to test for the presence or absence of seasonality in time series data and to estimate a DTDS model for the Plano Sales Tax Revenue data We are also going to identify the strong versus the weak seasons during the year as it relates to this data You are to hand in this exercise in class on Thursday September 25 You are to use the SAS program Plano Test Seasonality sas to complete this exercise a Using the first Proc Reg output fill in the blanks in the below Durbin Watson table The REG Procedure Model MODEL1 Dependent Variable rev Durbin Watson D 1 532 Pr DW Pr DW Number of Observations 1st Order Autocorrelation 190 0 225 Note Pr DW is the p value for testing positive autocorrelation and Pr DW is the p value for testing negative autocorrelation Do the ordinary least squares residuals of our DTDS regression model seem to have autocorrelated errors Yes No Explain your answer b Using the first Proc Autoreg output fill in the blanks below Coefficient on t 2 variable T statistic on t 2 variable Therefore we need to include exclude the t 2 variable from further consideration c Using the second Proc Autoreg output the one without the t 2 term fill in the blanks below AR1 Coefficient T statistic on AR1 Coefficient Therefore this AR coefficient is is not statistically significant AR3 Coefficient T statistic on AR3 Coefficient Therefore this AR coefficient is is not statistically significant AR5 Coefficient T statistic on AR5 Coefficient Therefore this AR coefficient is is not statistically significant AR8 Coefficient T statistic on AR8 Coefficient Therefore this AR coefficient is is not statistically significant AR10 Coefficient T statistic on AR10 Coefficient Therefore this AR coefficient is is not statistically significant AR12 Coefficient T statistic on AR12 Coefficient Therefore this AR coefficient is is not statistically significant Fill in the blanks in the below Durbin Watson table based on the Generalized least squares residuals Durbin Watson Statistics Order DW Pr DW Pr DW 1 1 9442 0 6594 2 0 6132 0 3868 3 2 1030 0 7982 4 1 8571 0 2159 0 7841 NOTE Pr DW is the p value for testing positive autocorrelation and Pr DW is the p value for testing negative autocorrelation True or False Given the results in parts a and c above it is obvious that we should be basing our statistical conclusions on generalized least squares statistics Proc Autoreg rather than ordinary least squares statistics Proc Reg Explain your answer d Using the second Proc Autoreg output we can see that individual t statistics indicate that the seasonal dummies are statistical significant at the 5 level 2 In the below space write out in conventional form the model we have used Generalized least squares to fit the data including the coefficient estimates and the t statistics in parentheses below the estimates Be sure to write out the AR 1 3 5 8 10 12 model for the errors as well e A comprehensive test of the significance of seasonality in the Plano Tax Revenue data is based on an overall test of the following hypotheses using Generalized least squares Proc Autoreg H 0 2 3 12 0 No seasonality H 1 At least one of the above s is not equal to zero Seasonality is present Fill in the following F table for this test Test Joint Test for Seasonality Source Numerator DF Mean F Value Pr F Square 11 1 5376516E12 0001 Denominator 171 42685238643 Therefore we should accept reject the null hypothesis of no seasonality and should accept reject the alternative hypothesis of seasonality in the Plano Tax Revenue data because f According to the Standardized seasonal effects by month table generated by the Plano Test Seasonality sas program the strong months in terms of the collection of tax revenue by Plano are The weak months are The strongest month is The weakest month is 3