A Cascade Linear Filter to Reduce Revisions and False Turning Points for Real Time Trend-Cycle Estimation

The problem of identifying the direction of the short-term trend (nonstationary mean) of seasonally adjusted series contaminated by high levels of variability has become of relevant interest in recent years. In fact, major financial and economic changes of global character have introduced a large amount of noise in time series data, particularly, in socioeconomic indicators used for real time economic analysis. The aim of this study is to construct a cascade linear filter via the convolution of several noise suppression, trend estimation, and extrapolation linear filters. The cascading approach approximates the steps followed by the nonlinear Dagum (1996) trend-cycle estimator, a modified version of the 13-term Henderson filter. The former consists of first extending the seasonally adjusted series with ARIMA extrapolations, and then applying a very strict replacement of extreme values. The nonlinear Dagum filter has been shown to improve significantly the size of revisions and number of false turning points with respect to H13. We construct a linear approximation of the nonlinear filter because it offers several advantages. For one, its application is direct and hence does not require some knowledge on ARIMA model identification. Furthermore, linear filtering preserves the crucial additive constraint by which the trend of an aggregated variable should be equal to the algebraic addition of its component trends, thus avoiding the selection problem of direct versus indirect adjustments. Finally, the properties of a linear filter concerning signal passing and noise suppression can always be compared to those of other linear filters by means of spectral analysis.