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...

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...

Derivations are offered for the LIML and the 2SLS estimators of single equations of the classical econometric simultaneous-equation system that differ from the usual ones. By assimilating both estimators to the method of moments, their essential similarities are highlighted. The LIML estimator...

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...