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.

The Wiener-Kolmogorov signal extraction filters, which are widely used in econometric analysis, are constructed on the basis of statistical models of the processes generating the data. In this paper, such models are used mainly as heuristic devices that are to be specified in whichever ways are...

In this paper, we analyse anew the relationship between aggregate income and consumption in the United Kingdom. Our analysis entails a close examination of the structure of the data, for which we employ a variety of spectral methods which depend on the concepts of Fourier analysis. We discover...

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...

This paper gives an account of some techniques for designing recursive frequency-selective filters which can be applied to data sequences of limited duration which may be nonstationary. The designs are based on the Wiener-Kolmogorov theory of signal extraction which employs a statistical model...

In this paper, we portray the essential features of the finite-sample signal extraction problem in both the stationary and the nonstationary cases. The computational procedures can be simplified in the light of our analysis. An important outcome of the analysis is a demonstration that the...

This paper sets forth some of the salient results in the algebra of circulant matrices which can be used in time-series analysis. It provides easy derivations of some results that are central to the analysis of statistical periodograms and empirical spectral density functions. A statistical test...

The income cycles that have been experienced by six OECD countries over the past 24 years are analysed. The amplitude of the cycles relative to the level of aggregate income varies amongst the countries, as does the degree of the damping that affects the cycles. The study aims to reveal both of...

The conventional dyadic multiresolution analysis constructs a succession of frequency intervals in the form of (<i>π</i> / 2^<i> j</i>, <i>π</i> / 2^{<i> j</i> - 1}); <i>j</i> = 1, 2, . . . , <i>n</i> of which the bandwidths are halved repeatedly in the descent from high frequencies to low frequencies. Whereas this scheme...