Concurrent research documents sizeable changes in the volatility of U.S. macroeconomic time series; e.g., see Kim and Nelson (1999), McConnell and Pérez-Quirós (2000), Stock and Watson (2002), and Sensier and van Dijk (2004). Most of the evidence from this literature suggests a sizeable reduction in volatility for many series; many of them used to construct business cycle indicators. With the e...

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...

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...

The paper illustrates and compares estimation methods alternative to maximum likelihood, among which multistep estimation and leave-one-out cross-validation, for the purposes of signal extraction, and in particular the separation of the trend from the cycle in economic time series, and longrange forecasting, in the presence of a misspecified, but simply parameterised model. Our workhorse models...

Trend elimination and business cycle estimation are analyzed by finite sample asymptotic methods. An overview history is provided, operator theory developed, limit as the size derived, filtered series properties studied relative to smoothing parameter () behavior. Simulations reveal that with delivers excellent approximations HP filter for common sizes but fails remove stochastic trends, contra...