Problem 1: Coast Insurance, Inc. is interested in forecasting annual larceny theft in the United States using the following data
|
Year
|
Larceny Theft*
|
Year
|
Larceny Theft*
|
|
1972
|
4,151
|
1984
|
6,592
|
|
1973
|
4,348
|
1985
|
6,926
|
|
1974
|
5,263
|
1986
|
7,257
|
|
1975
|
5,978
|
1987
|
7,500
|
|
1976
|
6,271
|
1988
|
7,706
|
|
1977
|
5,906
|
1989
|
7,872
|
|
1978
|
5,983
|
1990
|
7,946
|
|
1979
|
6,578
|
1991
|
8,142
|
|
1980
|
7,137
|
1992
|
7,915
|
|
1981
|
7,194
|
1993
|
7,821
|
|
1982
|
7,143
|
1994
|
7,876
|
|
1983
|
6,713
|
|
|
* Data are in thousands
Source: U.S Bureau of the Census
a. Prepare a time-series plot of these data. On the basis of this graph, do you think there is a trend in the data? Explain.
b. Look at the autocorrelation structures of larceny theft for lags of 1, 2, 3, 4, and 5. Do the autocorrelation coefficients fall quickly toward zero? Demonstrate that the critical value for rk is 0.417. Explain what these result tell you about a trend in the data.
c. On the basis of what is found in parts a and b, suggest a forecasting methods from Table that you think might be appropriate for this series.
Problem 2: Use exploratory data analysis to determine whether there is a trend and/or seasonality in mobile home shipments (MHS). The data by quarter are shown in the following table:
|
Year
|
Q1
|
Q2
|
Q3
|
Q4
|
|
1981
|
54.9
|
70.1
|
65.8
|
50.2
|
|
1982
|
53.3
|
67.9
|
63.1
|
55.3
|
|
1983
|
63.3
|
81.5
|
81.7
|
69.2
|
|
1984
|
67.8
|
82.7
|
79.0
|
66.2
|
|
1985
|
62.3
|
79.3
|
76.5
|
65.5
|
|
1986
|
58.1
|
66.8
|
63.4
|
56.1
|
|
1987
|
51.9
|
62.8
|
64.7
|
53.5
|
|
1988
|
47.0
|
60.5
|
59.2
|
51.6
|
|
1989
|
48.1
|
55.1
|
50.3
|
44.5
|
|
1990
|
43.3
|
51.7
|
50.5
|
42.6
|
|
1991
|
35.4
|
4.4
|
47.2
|
40.9
|
|
1992
|
43.0
|
52.8
|
57.0
|
57.6
|
|
1993
|
56.4
|
64.3
|
67.1
|
66.4
|
|
1994
|
69.1
|
78.7
|
78.7
|
77.5
|
|
1995
|
79.2
|
86.8
|
87.6
|
86.4
|
On the basis of your analysis, do you think is a significant trend in MHS? There seasonality? What forecasting methods might be appropriate for MHS according to the guideline in Table?