406 – Seasonal Time Series, Goodness-of-Fit, and Unit Root
New Results on Linear Filters Minimizing Phase-Shift for Seasonal Adjustment
Michel Grun-Rehomme
Fabien Guggemos
Insee
Dominique Ladiray
INSEE
Moving averages or linear filters are ubiquitous in seasonal adjustment and business cycle extraction methods. For example, software packages like X-12-Arima or Tramo-Seats use Henderson's and composite moving averages to estimate the main components of a time series, notably by accounting for forecasts obtained from an ARIMA modelling. When estimating the most recent points, all these methods must rely on asymmetric filters, whose main drawback is to induce phase shift effects that usually impact the real-time estimation of turning points. Here, we first propose a timeliness criterion included in a global procedure to compute moving averages minimizing the phase shift. Second, by drawing up a general unifying framework, we get a theoretical link between this way of designing moving averages, the filters based on minimized revisions purposes and a recently developed data-driven procedure called the Generalized Direct Filter Approach. Consequently, we also show that the results obtained for moving averages can be easily extended to any kind of linear filters, like the Hodrick-Prescott filter. Empirical results and comparisons on real time series data will be eventually presented.
