1. CoastCo Insurance, Inc., is interested in forecasting annual larceny thefts in the United States using the following data:
|
Year
|
Larceny
Thefts*
|
Year
|
Laetetty
Thefts*
6,592
6,926
|
|
t972
1973
|
|
1984
P965
|
|
1974
|
5,263
|
1986
|
7,257
|
|
1975
|
5.9713
|
1987
|
7,SM
|
|
1976
|
6.271
|
1988
|
7,706
|
|
1977
|
5,906
|
1989
|
7,1372
|
|
1978
|
5,083
|
1998
|
7,946
|
|
1979
|
6,578
|
1991
|
8,142
|
|
1980
|
7,137
|
1992
|
7,915
|
|
1981
|
7,194
|
1993
|
7,021
|
|
1982
|
7.143
|
1994
|
7,876
|
|
1983
|
6,713
|
|
|
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 structure of larceny thefts for lags of 1, 2, 3, 4, and 5. Do the autocorrelation coef?cients fall quickly toward zero? Demonstrate that the critical value for rk is 0.417. Explain what these results tell you about a trend in the data.
c. On the basis of what is found in parts a and b, suggest a forecasting method from Table 2.1 that you think might be appropriate for this series.
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
|
|
Quarter
|
|
|
Q1
|
Q2
|
Q3
|
Q4
|
|
1981
|
'54.9
|
70.1
|
65 8
|
50 2
|
|
1982
|
53.3
|
67 9
|
63 1
|
55 3
|
|
1983
|
613
|
811
|
817
|
691
|
|
1984
|
67.8
|
82.7
|
79 0
|
661
|
|
1985
|
62 3
|
79.3
|
76 5
|
65 S
|
|
|
|
1986
|
58.1
|
66 8
|
63 4
|
56 I
|
|
1987
|
51.9
|
628
|
647
|
53S
|
|
1988
|
187.0
|
605
|
99 2
|
51 6
|
|
1989
|
48.1
|
5S 1
|
59 3
|
44 5
|
|
1990
|
43 3
|
51 7
|
50 5
|
42 6
|
|
1991
|
354
|
474
|
472
|
409
|
|
1992
|
430
|
52.8
|
570
|
576
|
|
1993
|
56 4
|
64 3
|
62 1
|
66 4
|
|
1994
|
691
|
78.7
|
78.7
|
775
|
|
1995
|
79 2
|
86 8
|
87.6
|
664
|
On the basis of your analysis, do you think there is a signi?cant trend in MHS? Is there seasonality? What forecasting methods might be appropriate for MHS according to the guidelines in Table 2.1?
3. Home sales are often considered an important determinant of the future health of the economy. Thus, there is widespread interest in being able to forecast total houses sold (THS). Quarterly data for THS are shown in the following table in thousands of units:
a. Prepare a time-series plot of THS. Describe what you see in this plot in terms of trend and seasonality.
b. Calculate and plot the ?rst twelve autocorrelation coef?cients for PHS. What does this autocorrelation structure suggest about the trend?
c. De-trend the data by calculating ?rst differences: DTHSt THSt THSt1. Calculate and plot the ?rst eight autocorrelation coef?cients for DTHS. Is there a trend in DTHS?
4. Question 1 includes data on the Japanese exchange rate (EXRJ) by month. On the basis of a time-series plot of these data and the autocorrelation structure of EXRJ, would you say the data are stationary? Explain your answer.