For this paper I have gathered quarterly data on the sales of Calloway Golf Company from 1995 to the third quarter of 1999,and will attempt to fit a time series model using the Classical Decomposition Method, which uses a multifactor model shown below:

Yt = actual value of the time series at time t

The trend component (T) in a time series is the long-run general movement

caused by long-term economic, demographic, weather and technological movements. The cyclical component (C) is an influence of about three to nine years caused by economic, demographic, weather, and technological changes in an industry or economy. The seasonal variations (S) are the result of weather and man-made conventions such as holidays. These can occur every year, month week, or 24 hours. The error term (e) is simply the residual component of a time series that is not explained by T, C, and S.

There are two general types of decomposition models that can be used. They are the additive and multiplicative decomposition models.

In the multiplicative decomposition model, which is the most frequently used model, Y is a product of the four components, T, C, S, and e. C and S are indexes that are proportions centered on 1. Only the trend, T, is measured in the same units as the items being forecasted.

The first step in the decomposition method is to find the seasonal indexes, as shown in table 1, in this case by performing a four-period moving average and using a method called the ratio to moving average method. It is necessary to measure the seasonality first because it is difficult to measure the trend of a highly seasonal series. By looking at the final seasonal indexes we can see that there is seasonality in the series, because the indexes are smaller in the first and fourth quarters. One would expect this, because the sales of golf equipment are more likely to occur in the spring and summer, rather than the fall and winter. Once the final seasonal indexes are calculated and adjusted we can move on to the next step of the decomposition method.

Like the multiplicative method, we must first calculate a four-period moving average and center it to estimate the trend cycle. Next we must subtract the centered moving average from the actual sales to obtain the seasonal error factor for each period. Next, we use these error terms to calculate the unadjusted seasonal indexes. This is where the methods in the two models differ. The mean of the unadjusted seasonal indexes must be determined and then subtracted from each of the unadjusted terms to calculate the final seasonal indexes. In the additive model, the sum of the final seasonal indexes must be equal to 0. All of this is shown at the bottom of table 5.

The next step in the multiplicative decomposition model is to calculate the fitted values (TS) by multiplying the trend (T) by its appropriate seasonal factor. This is

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Approximate Word count = 1271
Approximate Pages = 5 (250 words per page double spaced)