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
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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•
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References
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Book•
03 Jan 2001
TL;DR: The history of multivariate polynomial interpolation can be found in this article, where the authors present a survey of interpolation by algebraic polynomials and their applications.
Abstract: Preface: Numerical Analysis 2000. Vol. II: Interpolation and extrapolation (C. Brezinski). Convergence Acceleration during the 20th century (C. Brezinski). On the history of multivariate polynomial interpolation (M. Gasca, T. Sauer). Elimination techniques: from extrapolation to totally positive matrices and CADG (M. Gasca, G. Muhlbach). The ipsilon algorithm and related topics (P.R. Graves-Morris, D.E. Roberts, A. Salam). Scalar Levin-type sequence transformations (H.H.H. Homeier). Vector extrapolation methods. Applications and numerical comparison (K. Jbilou, H. Sadok). Multivariate Hermite interpolation by algebraic polynomials: A survey (R.A. Lorentz). Interpolation by Cauchy-Vandermonde systems and applications (G. Muhlbach). The E-algorithm and the Ford-Sidi algorithm (N. Osada). Diophantine approximations using Pade approximations (M. Prevost). The generalized Richardson extrapolation process GREP(1) and computation of derivatives of limits of sequences with applications to the d(1)-transformation (A. Sidi). Matrix Hermite-Pade problem and dynamical systems (V. Sorokin, J. Van Iseghem). Numerical analysis of the non-uniform sampling problem (T. Strohmer). Asymptotic expansions for multivariate polynomial approximation (G. Walz). Prediction properties of Aitken's iterated 2 process, of Wynn's epsilon algorithm, and of Brezinski's iterated theta algorithm (E.J. Weniger).
99 citations
TL;DR: In this article, the economic interpretation of the unobserved components model was examined in the light of the apparent problem posed by previous work in that several practiced methodologies seem to lead to very different models of certain economic variables.
Abstract: This paper deals with the economic interpretation of the unobserved components model in the light of the apparent problem posed by previous work in that several practiced methodologies seem to lead to very different models of certain economic variables. A detailed empirical analysis is carried out to show how the failure in obtaining quasi-orthogonal components can seriously bias the interpretation of some decomposition procedures. Finally, the forecasting performance (in both the short and long run) of these decomposition models is analyzed in comparison with other alternatives.
23 citations