Question #31

of 101 The table below shows the autocorrelations of the lagged residuals for quarterly theater ticket sales that were estimated using the AR(1) model: ln(salest) = b0 + b1(ln salest − 1) + et. Assuming the critical t-statistic at 5% significance is 2.0, which of the following is the most likely conclusion about the appropriateness of the model? The time series: Lagged Autocorrelations of the Log of Quarterly Theater Ticket Sales Lag Autocorrelation Standard Error t-Statistic 1 −0.0738 0.1667 −0.44271 2 −0.1047 0.1667 −0.62807 3 −0.0252 0.1667 −0.15117 4 0.5528 0.1667 3.31614 A) contains seasonality. B) contains ARCH (1) errors. C) would be more appropriately described with an MA(4) model. Winston Collier, CFA, has been asked by his supervisor to develop a model for predicting the warranty expense incurred by Premier Snowplow Manufacturing Company in servicing its plows. Three years ago, major design changes were made on newly manufactured plows in an effort to reduce warranty expense. Premier warrants its snowplows for 4 years or 18,000 miles, whichever comes first. Warranty expense is higher in winter months, but some of Premier's customers defer maintenance issues that are not essential to keeping the machines functioning to spring or summer seasons. The data that Collier will analyze is in the following table (in $ millions): Quarter Warranty Expense Change in Warranty Expense yt Lagged Change in Warranty Expense yt-1 Seasonal Lagged Change in Warranty Expense yt-4 2002.1 103 2002.2 52 –51 2002.3 32 –20 –51 2002.4 68 +36 –20 2003.1 91 +23 +36 2003.2 44 –47 +23 –51 2003.3 30 –14 –47 –20 2003.4 60 +30 –14 +36 2004.1 77 +17 +30 +23 2004.2 38 –39 +17 –47 2004.3 29 –9 –39 –14 2004.4 53 +24 –9 +30 Winston submits the following results to his supervisor. The first is the estimation of a trend model for the period 2002:1 to 2004:4. The model is below. The standard errors are in parentheses. (Warranty expense)t = 74.1 - 2.7* t + et (14.37) (1.97) R-squared = 16.2% Winston also submits the following results for an autoregressive model on the differences in the expense over the period 2004:to 2004:4. The model is below where "y" represents the change in expense as defined in the table above. The standard errors are in parentheses. yt = -0.7 - 0.07* yt-1 + 0.83* yt-4 + et (0.643) (0.0222) (0.0186) R-squared = 99.98% After receiving the output, Collier's supervisor asks him to compute moving averages of the sales data.