# Classical Decomposition Model

Classical Decomposition Method for Calloway Golf (1995-1999)
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.
Multiplicative:Y =T * C * S * e
As you can see above the type of seasonality can be determined by looking at the plot of the data.The determination of whether seasonal influences are additive or multiplicative is usually evident from the plot of the data, but this is not the case with the data for Calloway as you can see from thefirst graph of the quarterly sales. While it is my pretension that the seasonal influences for Calloway are multiplicative, I will use both methods and compare the two models to determine which is a better fit for the quarterly data for Calloway Golf.
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