Comparison of efficient seasonal indexes

Estimates of a seasonal index in the standard manner (from a moving average) introduce systematic error into the seasonal estimates if a trend is present. This paper shows that a logarithmic modification of the standard moving average procedure will cause it to be consistent with a trend and is an efficient alternative. This paper also compares several other efficient seasonal indexing procedures appropriate for routine business applications and shows some numerical results. The results indicate that it is possible to achieve an improvement in the precision of the seasonal index, in the seasonally adjusted data and in forecasts based upon this data, by considering logarithmic alternatives to standard seasonal indexing procedures. This improvement may be accomplished without a substantial increase in complexity or in the associated computational burden. The opportunities for improvement are shown to be greatest when the data contain substantial trend and seasonal aspects and when the trend has a percentage form. Some suggestions for forecasters are offered.