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 paper investigates strategies for real-time estimation of the output gap. First, I examine estimates from univariate models with stochastic cycles. This corresponds to the use of model-based band-pass filters in real-time, and I find that the turning points in real-time and final output gap...

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...

A class of model-based filters for extracting trends and cycles in economic time series is presented. These lowpass and bandpass filters are derived in a mutually consistent manner as the joint solution to a signal extraction problem in an unobserved-components model. The resulting trends and...

This article develops a new method for detrending time series. It is shown how, in a Bayesian framework, a generalized version of the Hodrick-Prescott filter is obtained by specifying prior densities on the signal-to-noise ratio (q) in the underlying unobserved components model. This helps...

Oil prices clearly play an important role in the macroeconomy. The dynamics of oil prices have, however, been difficult to pin down because of the frequent occurrence of large shocks. In this paper, we propose a time series model with heavy-tailed disturbances to analyze the dynamics of the oil...