Seasonal adjustment and kalman filtering: Extension to periodic variances

This paper reviews the relations between the methods of seasonal adjustment used by official statistical agencies and the ‘model-based’ methods that postulate explicit stochastic models for the unobserved components of a time series and apply optimal signal extraction theory to obtain a seasonally adjusted series. The Kalman filter implementation of the model-based methods is described and some recent results on its properties are reviewed. The model-based methods employ homogeneous or time-invariant models that assume in particular that the autocovariance structure does not vary with the season. Relaxing this leads to the class of models known as periodic models, and an example of a seasonally heterosceclastic unobserved-components ARIMA (SHUCARIMA) model is presented. The calculation of the standard error of a seasonally adjusted series via the Kalman filter is extended to this periodic model and illustrated for a monthly rainfall series.