JSM 2004 - Toronto

Abstract #300913

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Activity Number: 73
Type: Topic Contributed
Date/Time: Monday, August 9, 2004 : 8:30 AM to 10:20 AM
Sponsor: Business and Economics Statistics Section
Abstract - #300913
Title: An Iterated Parametric Approach to Nonstationary Signal Extraction
Author(s): Tucker S. McElroy*+
Companies: U.S. Census Bureau
Address: Statistical Research Division, Washington, D.C., DC, 20233-9100,
Keywords: ARIMA component model ; nonstationary time series ; seasonal adjustment ; signal extraction ; Wiener-Kolmogorov filtering ; X-11
Abstract:

Consider the three-component time series model that decomposes observed data (Y) into the sum of seasonal (S), trend (T), and irregular (I) portions. Assuming that S and T are nonstationary, it is demonstrated that widely used Wiener-Kolmogorov signal extraction estimates of S and T are related by simple formulas, and can be obtained through an appropriately initialized iteration scheme applied to optimal estimates derived from reduced two-component models Y^S and Y^T consisting of S plus I and T plus I, respectively; this "bootstrapping" signal extraction methodology is reminiscent of X-11's iterated nonparametric approach. The contraction-mapping analysis of the iteration scheme provides geometric intuition for the algebraic relationship between full-model and reduced-model signal extraction estimates.

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