Variance intervention is a simple state-space approach to handling sharp discontinuities of level or slope in the states or parameters of models for non-stationary time-series. It derives from earlier procedures used in the 1960s for the design of self-adaptive, state variable feedback control systems. In the alternative state-space forecasting context considered in the present paper, it is particularly useful when applied to structural time series models. The paper compares the variance intervention procedure with the related 'subjective intervention' approach proposed by West and Harrison in a recent issue of the Journal ofForecusting, and demonstrates it efficacy by application to various time-series data, including those used by West and Harrison. KEY WORDS State-space methods Recursive estimation Fixed interval smoothing Structural models Non-stationary time-series Intervention methods Spectral properties Lag-free filtering Adaptive seasonal adjustment
The paper on 'subjective intervention' by West and Harrison (1989), and the related paper by Jun (1989), which appear in a recent issue of the Journal of Forecasting, show how conveniently the recursive approach to time-series analysis and forecasting allows for intervention by the analyst. However, while the specific 'subjective intervention' approach suggested by West and Harrison has value in the kind of applications they discuss, the general concept which lies behind their proposals is well established, and its use in various areas of systems analysis can be tracked back to the early 1960s, shortly after the appearance of Kalman's seminal paper on state variable filtering in 1960. Moreover, some of this earlier work can help to indicate how certain simplifications can be introduced into the implementation of these kind of recursive algorithms; simplifications which can aid the user and, at the same time, make the analysis somewhat more objective, if this is desired.
In this paper we describe briefly a method of intervention analysis that has some close similarity with that of West and Harrison (hereafter referred to as WH) and which we have termed variance intervention (Young, P. C . , 1987(Young, P. C . , , 1988;;Ng, 1987). This method forms part of a unified, recursive approach to time-series analysis, forecasting and seasonal adjustment developed during the last few years at Lancaster (see also: Young and Ng, 1988; Ng and Young,