Question #30
Reading: Reading 2 Time-Series Analysis
PDF File: Reading 2 Time-Series Analysis.pdf
Page: 14
Status: Unattempted
Correct Answer: A
Question
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
Answer Choices:
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
Explanation
The time series contains seasonality as indicated by the strong and significant
autocorrelation of the lag-4 residual.
(Module 2.4, LOS 2.l)
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.