Production and Operations Management Consulting.
Time series analysis: Ratio-to-moving-average procedure
The components of a time series are computed according to the ratio-to-moving-average 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 ratio-to-moving-average method, the following steps are performed: First, a centered moving-average 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.
|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 ".