POM Prof. Tempelmeier GmbH
Production and Operations Management Consulting.
Time series analysis: Ratiotomovingaverage procedure
The components of a time series are computed according to the ratiotomovingaverage method. The number of saesonal periods may be 4 or 12. If a different number of seasonal periods is entered (e.g. 0), then the deseasonalization procedure is skipped and only the trend line is computed by linear regression.
According to the ratiotomovingaverage method, the following steps are performed: First, a centered movingaverage is computed to find the smooth component TC of the time series. Next, the seasonal factors SI are computed through the division SI=Y/TC. Then, for each seasonal period the seasonal factor is estimated. Seasonal factors are not standardized. Finally, the trend line is computed by linear regression.
Symbols:
t  index of time periods 
tc(t)  smooth component in period t 
si(t)  seasonal factor in period t 
su(t)  mean seasonal factor with respect to the season of period t 
tci(t)  deseasonalized time series in period t 
rho(j)  autocorrelation coeffizient given a time lag of j periods 
The seasonal factors and the parameters of trend line are automatically transfered as initial values into the module "Procedure of Winters ".
