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This paper sets out the theoretical foundations for continuous-time signal extraction in econo- metrics. Continuous-time modeling gives an efiective strategy for treating stock and ∞ow data, irregularly spaced data, and changing frequency of observation. We rigorously derive the op- timal continuous-lag fllter when the signal component is nonstationary, and provide several illustrations, including a new class of continuous-lag Butterworth fllters for trend and cycle estimation.

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