The Kalman filter—or, more precisely, the extended Kalman filter (EKF)—is a fundamental engineering tool that is pervasively used in control and robotics and for various estimation tasks in autonomous systems. The recently developed field of invariant extended Kalman filtering uses the...

In the classical Kalman-Bucy filter and in the subsequent literature so far, it has been assumed that the initial value of the signal process is independent of both the noise of the signal and of the noise of the observations.The purpose of this paper is to prove a filtering equation for a...

A problem often faced by economic researchers is the interpolation or distribution of economic time series observed at low frequency into compatible higher frequency data. A method based on wavelet analysis is presented to temporal disaggregate time series. A standard `plausible' method is...

Using recent advances in time-varying spectral methods, this research analyses the growth cycles of the core of the euro area in terms of frequency content and phasing of cycles. The methodology uses the continuous wavelet transform (CWT) and also Hilbert wavelet pairs in the setting of a...

This note gives a fairly complete statistical description of the Hodrick-Prescott Filter (1997), originally proposed by Leser (1961). It builds on an approach to seasonal adjustment suggested by Leser (1963) and Schlicht (1981, 1984). A moments estimator for the smoothing parameter is proposed...