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

34 Pages Posted: 17 Jul 2008

See all articles by Tucker McElroy

Tucker McElroy

U.S. Census Bureau - Center for Statistical Research and Methodology

Thomas M. Trimbur

University of Cambridge - Faculty of Economics and Politics

Date Written: December 1, 2007

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.

Keywords: Continuous time processes, cycles, Hodrick-Prescott filter, linear filtering, signal extraction, turning points

JEL Classification: C22, E32

Suggested Citation

McElroy, Tucker and Trimbur, Thomas M., Continuous Time Extraction of a Nonstationary Signal with Illustrations in Continuous Low-Pass and Band-Pass Filtering (December 1, 2007). FEDS Working Paper No. 2007-68, Available at SSRN: https://ssrn.com/abstract=1161216 or http://dx.doi.org/10.2139/ssrn.1161216

Tucker McElroy

U.S. Census Bureau - Center for Statistical Research and Methodology ( email )

4600 Silver Hill Road
Washington, DC 20233-9100
United States

Thomas M. Trimbur (Contact Author)

University of Cambridge - Faculty of Economics and Politics ( email )

Austin Robinson Building
Sidgwick Avenue
Cambridge, CB3 9DD
United Kingdom

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