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An Iterated Parametric Approach to Nonstationary Signal Extraction

Tucker McElroy and Andrew Sutcliffe

KEY WORDS: ARIMA component model, nonstationary time series, seasonal adjustment, signal extraction, Wiener-Kolmogorov Filtering, X-11


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 and that I is stationary, it is demonstrated that widely-used Wiener-Kolmogorov signal extraction estimates of S and T can be obtained through an iteration scheme applied to optimal estimates derived from reduced two-component models for YS = S+YT = T+I. This "bootstrapping" signal extraction methodology is reminiscent of the iterated nonparametric approach of the U.S. Census Bureau's X-11 program. The analysis of the iteration scheme provides insight into the algebraic relationship between full model and reduced model signal extraction estimates.


Source: U.S. Census Bureau, Statistical Research Division

Created: September 30, 2004
Last revised: March 3, 2005

Source: U.S. Census Bureau | Statistical Research Division | (301) 763-3215 (or |   Last Revised: October 08, 2010