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Journal ArticleDOI

Filters for Short Nonstationary Sequences

AbstractThis paper describes a methodology for implementing bidirectional frequency-selective filters in cases where the data sequence is short and nonstationary. A simple method is proposed for dealing with the start-up problem. The method has a firm theoretical basis and it is computationally efficient.

Topics: Linear filter (51%)

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Citations
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Journal ArticleDOI
TL;DR: The areas in which econometricians have made contributions are emphasised, which include the methods for handling the initial-value problem associated with nonstationary processes and the algorithms of fixed-interval smoothing.
Abstract: An account is given of recursive regression and of Kalman filtering which gathers the important results and the ideas that lie behind them within a small compass. It emphasises the areas in which econometricians have made contributions, which include the methods for handling the initial-value problem associated with nonstationary processes and the algorithms of fixed-interval smoothing.

8 citations



References
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Journal ArticleDOI
Abstract: In this paper we generalize the results of [4] and modify the algorithm presented there to obtain a better rate of convergence.

2,163 citations


Book
21 Nov 1983
Abstract: Prediction and Regulation by Linear Least-Square Methods was first published in 1963. This revised second edition was issued in 1983. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions.During the past two decades, statistical theories of prediction and control have assumed an increasing importance in all fields of scientific research. To understand a phenomenon is to be able to predict it and to influence it in predictable ways. First published in 1963 and long out of print, Prediction and Regulation by Linear Least-Square Methods offers important tools for constructing models of dynamic phenomena. This elegantly written book has been a basic reference for researchers in many applied sciences who seek practical information about the representation and manipulation of stationary stochastic processes. Peter Whittle's text has a devoted group of readers and users, especially among economists. This edition contains the unchanged text of the original and adds new works by the author and a foreword by economist Thomas J. Sargent.

330 citations


Journal ArticleDOI
Abstract: The Kalman recursion for state space models is extended to allow for likelihood evaluation and minimum mean square estimation given states with an arbitrarily large covariance matrix. The extension is computationally minor. Application is made to likelihood evaluation, state estimation, prediction and smoothing.

308 citations


Posted Content
Abstract: We propose a procedure for representing a time series as the sum of a smoothly varying trend component and a cyclical component. We document the nature of the co-movements of the cyclical components of a variety of macroeconomic time series. We find that these co-movements are very different than the corresponding co-movements of the slowly varying trend components.

275 citations


Book
01 Jan 1999
TL;DR: Introduction.
Abstract: Introduction. Polynomial Methods. Least-Square Methods. Fourier Methods. Time-Series Models. Time-Series Estimation. Statistical Appendix: On Disk.

265 citations