Asymmetric Moving Averages Minimizing Phase-Shift

• Activity Number: 464
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Dominique Ladiray+ and Michel Grun-Rehomme*
• Companies: INSEE and ENSAE
• Keywords: Seasonal adjustment ; asymmetric moving averages ; phase-shift ; turning point detection

Abstract

Henderson's moving averages are used in X-12-Arima, with composite moving averages, to estimate the main components of a time series. For the estimation of the most recent points, X-12-Arima applies symmetric averages on forecasts obtained from an ARIMA modelling of the series. As forecasted values are linear combinations of past values, it turns out that X-12-Arima applies asymmetric moving averages at the end of the series. If these asymmetric moving averages have good properties regarding the size of future revisions due to the seasonal adjustment process, they also induce phase shifts that usually impacts the real-time estimation of turning points. we propose a timeliness criteria which allows computing moving averages minimizing the phase shift. We focus here on moving averages whose coefficients do not depend on the characteristics of the series.