On the basis of your analysis do you think is a significant

Question

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 r_k 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?