Multipass Seasonal Adjustment Filter

Abstract

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.