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X-13ARIMA-SEATS Seasonal Adjustment Program

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Matrix Formulas for Nonstationary ARIMA Signal Extraction

Tucker S. McElroy (1)


The paper provides general matrix formulas for minimum mean squared error signal extraction, for a finitely sampled time series whose signal and noise components are nonstationary ARIMA processes. These formulas are quite practical; as well as being simple to implement on a computer, they make it possible to easily derive important general properties of the signal extraction filters. We also extend these formulas to estimates of future values of the unobserved signal, and show how this result combines signal extraction and forecasting.

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

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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