Filters for Short Nonstationary Sequences
TL;DR: In this article, a methodology for implementing bidirectional frequency-selective filters in cases where the data sequence is short and nonstationary is described, and a simple method is proposed for dealing with the start-up problem.
Abstract: This 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.
Figures (9)
Figure 8. The annual fluctuations in the atmospheric concentration of carbon dioxide which surround the upward trend. 
Figure 7. The residual sequence from detrending the temperature data. 
Figure 4. The gain of the Hodrick–Prescott lowpass 
Figure 9. The residual sequence from detrending the Swiss unemployment figures, which gives evidence of labour hoarding. 
Figure 5. The gain of the 6th order Butterworth lowpass filter with a cut-off frequency of π/8. 
Figure 6. The gain of the 8th order Butterworth lowpass filter with a cut-off frequency of 3π/8. 
Figure 1. Northern hemisphere temperature anomalies 1880–1990. 
Figure 3. The quarterly figures on Swiss unemployment from 1980.1 to 1996.2. 
Figure 2. Monthly atmospheric carbon dioxide concentrations in parts per million by volume from Jan. 1958 to Jan. 1984.
Citations
More filters
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
Journal Article•
2 citations
References
More filters
TL;DR: In this paper, the authors generalize the results of [4] and modify the algorithm presented there to obtain a better rate of convergence, which is the same as in this paper.
Abstract: In this paper we generalize the results of [4] and modify the algorithm presented there to obtain a better rate of convergence.
2,225 citations
Posted Content•
TL;DR: In this article, the authors propose a procedure for representing a time series as the sum of a smoothly varying trend component and a cyclical component, and find that these co-movements are very different than the corresponding co-movments of the slowly varying trend components.
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.
593 citations
Book•
21 Nov 1983
TL;DR: Prediction and Regulation by Linear Least-Square Methods (PRMLM) as mentioned in this paper is a well-known work in statistical analysis of stationary stochastic processes with a focus on prediction and control.
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
TL;DR: In this article, 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, and application is made to likelihood evaluation, state estimation, prediction and smoothing.
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.
314 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.
273 citations