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Continuous Time Extraction of a Nonstationary Signal with Illustrations in Continuous Low-pass and Band-pass Filtering

Tucker McElroy and Thomas Trimbur

KEY WORDS: signal extraction, continuous time processes, linear filtering, Hodrick-Prescott Filter, Band-Pass Filter

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.

CITATION:

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

Created: November 16, 2006
Last revised: November 16, 2006


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