Second-order properties for multiple-bilinear models

György Terdik

Journal of Multivariate Analysis, 1990, vol. 35, issue 2, 295-307

Abstract: Bilinear models which are defined as input-output (noise-observation in time series analysis) systems being linear with respect to each of the input and output when the other is fixed, arise in a natural way from basic principles in chemistry, physics, engineering, and several other fields of science. Most of the cases contain multiple output with interaction. In time series analysis it is necessary to consider the influence of other related time series to describe the structure of the model properly. The multiple bilinear models were recently investigated in the time domain. The method that was used only gives a sufficient condition and asymptotic results concerning the stationarity and the second-order properties. We deal with the frequency domain method, i.e., using the Wiener-Ito spectral representation, to describe the second-order properties, as this method was shown more informative in the scalar case. We give a necessary and sufficient condition for the second-order stationarity of multiple bilinear models in terms of the spectral radius of a particular matrix involving the coefficients of the model. The exact form of the spectral density function shows that there is no way one can discriminate between a linear (non-Gaussian) and a bilinear model based on the second-order properties of the process.

Keywords: bilinear; Model; stationarity; multiple; Wiener-Ito; integral; Wiener-Ito; spectral; representation (search for similar items in EconPapers)
Date: 1990
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