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MATRIX FORMULAS FOR NONSTATIONARY ARIMA SIGNAL EXTRACTION

Published online by Cambridge University Press:  04 April 2008

Tucker McElroy
Tucker McElroy*
Affiliation:
U.S. Census Bureau
*
Address correspondence to Tucker McElroy, Statistical Research Division, U.S. Census Bureau, 4700 Silver Hill Road, Washington, DC 20233-9100; e-mail: mcelroy@census.gov.
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Abstract

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 autoregressive integrated moving average processes. These formulas are quite practical; in addition to 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 we show how this result combines signal extraction and forecasting.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 4 , August 2008 , pp. 988 - 1009
Copyright
Copyright © Cambridge University Press 2008

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