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...

This article investigates a general class of stochastic cycles, presenting the main properties in the time and frequency domains. Harvey and Trimbur [Review of Economics and statistics (2003) Vol. 85, pp. 244-55] showed how generalized cyclical processes may be used in unobserved components...

The paper derives forecasting and signal extraction estimates for continuous time processes. We present explicit formulas for filters and filter kernels that yield minimum mean square error estimates of future values of the process or an unobserved component, based on a continuum of values in...