In the last thirty years there has been extensive research in the analysis of linear time series models. In analyzing univariate and multivariate time series the assumption of linearity is, in many cases, unrealistic. With this in view, recently, many nonlinear models for the analysis of time series have been proposed, mainly for univariate series. One class of models proposed which has received considerable interest, is the class of bilinear models. In particular has the theory of univariate bilinear time series been considered in a number of papers (d. Granger and Andersen (1978), Subba Rao (1981) and Bhaskara Rao et. al. (1983) and references therein); these models are analogues of the bilinear systems as proposed and studied previously by control theorists. Recently several analytic properties of these time series models have been investigated, and their estimation and applications have been reported in Subba Rao and Gabr (1983). But it is important to study the relationship between two or more time series, also 10 the presence of nonlinearity. Therefore, multivariate generalizations of the bilinear models have been considered by Subba Rao (1985) and Stensholt and Tj(llstheim (1985, 1987). Here we consider some theoretical aspects of multivariate bilinear time series models (such as strict and second order stationarity, ergodicity, invertibility, and, for special cases. strong consistency of least squares estimates). The theory developed is illustrated with simulation results. Two applications to real bivariate data (mink-muskrat data and "housing starts-houses soldll data) and the FORTRAN programs developed in this project are also included.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:582853 |
| Date | January 1989 |
| Creators | Stensholt, B. K. |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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