Continuous Time Extraction of a Nonstationary Signal with Illustrations in Continuous Low-pass and Band-pass Filtering
Continuous Time Extraction of a Nonstationary Signal with Illustrations in Continuous Low-pass and Band-pass Filtering
RRS2006-13
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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