Smoothing Seasonally Adjusted Time Series

• Activity Number: 407
• Type: Contributed
• Date/Time: Thursday, August 15, 2002 : 10:30 AM to 12:20 PM
• Sponsor: Business & Economics Statistics Section*
• Author(s): Estela Dagum*+ and Alessandra Luati
• Affiliation(s): University of Bologna and University of Bologna
• Keywords: Nonparametric smoothers ; Loess ; Gaussian kernel ; Fixed bandwidth ; Cubic smoothing spline ; Henderson filter

Abstract

This paper deals with the properties of several nonparametric linear filters for the smoothing of seasonally adjusted data, particularly, with regard to the type of signal passed and noise suppressed by each smoother. This is done by means of spectral techniques, analyzing the gain and phase shift functions of their corresponding symmetric and asymmetric weight systems. The smoothers discussed are Loess, the cubic smoothing spline, the Gaussian kernel, and the 13-term Henderson filter often applied by statistical agencies for trend-cycle estimation of monthly data. They are all constrained to be of a fixed length, equal to 13, to facilitate a comparison with the Henderson filter and to avoid a large number of end points estimated with asymmetric weights. Because of this constraint, some smoothers' statistical properties are not necessarily optimal as when their respective smoothing parameters are optimally estimated according to other criteria.