Data revisions with moving average seasonal adjustment procedures

Abstract

Most seasonal adjustment procedures make use of data both prior and subsequent to the datum being adjusted, as both future and past observations ordinarily contain information pertinent to seasonality at a given point in the series. In particular, when the series is generated by a stationary or homogeneously non-stationary stochastic process, the ‘reversibility’ of such a process gives rise to the result that the optimal (minimum mean square error) seasonal estimate is a weighted moving average of the series which is symmrtric in the future and past [Whittle (1963)]. However, for the seasonal adjustment of current or recent data and for forecasting seasonal factors [which are more important than historical seasonal adjustment for interpreting or reacting to movements in the series], the relevant future of the series is not yet available. Thus, based on the observations that are available, preliminary estimates of the seasonal component are made, which are subsequently recised as more series values are observed, perhaps repeatedly, until the unobserved future no longer contains significant relevant information. These revisions in seasonally adjusted data, or equivalently in seasonal factors or components, are the subject of this paper. A knowledge of the characteristics of the seasonal revisions can facilitate a better assessment of the relative quality of preliminary seasonally adjusted data. Knowing that the revisions are normally distributed with given variance, for example, would enable confidence bands for the final data to be constructed around the preliminary data. Sections 2, 3 and 4 of the paper develop a characterization of seasonal revisions in terms of stationary and non-stationary linear time series models, assuming that such models generate the series itself and the seasonal and