The consumption of turkey in the United States can be catego

The consumption of turkey in the United States can be categorized into three seasons: 1. Thanksgiving/Christmas; 2. Passover/Easter holiday; and 3. the remainder of the year. The turkey consumption (in pounds per month) for the previous four years is located in the table below.

Year

Season

lbs. / month

1

1

2.1

2

1.4

3

1.1

2

1

2.5

2

1.5

3

1.3

3

1

2.7

2

2.1

3

1.7

4

1

3.1

2

2.2

3

1.6

Before continuing to the problems below, construct a time series plot (line chart) of the turkey consumption data. Use the data and this chart to answer the questions below.

As an alternative to the multiple regression approach to forecasting U.S. turkey consumption, utilize the time series decomposition method to provide seasonal forecasts.

(a)Find the three-period centered moving averages (CMA).

(b)Compute the seasonal-irregular component.

(c)Compute the seasonal factors (seasonal indexes) for each season.

(d)Compute the deseasonalized time series for consumption (lbs./month).

(e)Estimate the linear trend from the deseasonalized consumption and comment on the significance (R-square and F-test) of the equation.

(f)Develop deseasonalized trend projections for each season (1, 2 and 3) of Year 5 based on the estimated linear trend.

(g)Use the seasonal indexes to adjust the linear trend projections developed in part (f) to account for the effect of season.

Solution