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Board of Governors of the Federal Reserve System (US)
Finance and Economics Discussion Series
Continuous time extraction of a nonstationary signal with illustrations in continuous low-pass and band-pass filtering
Tucker S. McElroy
Thomas M. Trimbur
Abstract

This paper sets out the theoretical foundations for continuous-time signal extraction in econometrics. Continuous-time modeling gives an effective strategy for treating stock and flow data, irregularly spaced data, and changing frequency of observation. We rigorously derive the optimal continuous-lag filter when the signal component is nonstationary, and provide several illustrations, including a new class of continuous-lag Butterworth filters for trend and cycle estimation.


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Tucker S. McElroy & Thomas M. Trimbur, Continuous time extraction of a nonstationary signal with illustrations in continuous low-pass and band-pass filtering, Board of Governors of the Federal Reserve System (US), Finance and Economics Discussion Series 2007-68, 2007.
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Keywords: Time-series analysis ; Econometrics
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