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X-13ARIMA-SEATS Seasonal Adjustment Program

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An Iterated Parametric Approach to Nonstationary Signal Extraction

Tucker S. McElroy (1) and Andrew Sutcliffe (2)

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 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.

KEYWORDS:

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





(1) Tucker S. McElroy is Mathematical Statistican, U. S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email : Tucker.S.McElroy@census.gov

(2) Andrew Sutcliffe is currently a statistican with the Austalian Bureau of Statistics. email: andrew.sutcliffe@abs.gov.au



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Source: U.S. Census Bureau | Center for Statistical Research and Methodology | (301) 763-1649 (or x12@census.gov) |  Last Revised: November 19, 2012