Multipass Seasonal Adjustment Filter

A state-space seasonal time series model and a new seasonal decomposition algorithm, based on the Kalman filter, are introduced. The time series model is statistically equivalent to the multiplicative seasonal model, ARIMA (0, 1, 1)(0, 1, 1)_s, of Box and Jenkins. It is shown that the steady-state filter's forecasts of this model are identical to the Box and Jenkins' values. The seasonal adjustment and decomposition algorithm is based on a multipass filtering technique for back forecasting and smoothing in order to correct start-up transients and replace lost filter's estimates during the initialization phase. The in-sample performances of this multipass seasonal adjustment filter (MSAF) are compared with the Census X-11 procedure, using real time series. The empirical results clearly show the superiority of the proposed method for all time series in the study. Additionally, a sample from the Makridakis-Hibon's 111 time series is used for ex-post forecasting evaluation of the proposed method in comparison to the Winters and simple ratio-to-moving-average methods. It is observed that the MSAF forecasts are better than its competitors in most cases, especially when leadtimes are at least one season length.