Abstract

This thesis is focused on the basis function method for the identification of nonstationary processes. The first chapter describes a group of models that can be identified using the basis function method. The next chapter describes the basic version of the basis function method, including its algebraic and statistical properties. The following section introduces the local basis function (LBF) method: its properties are described and similarities and differences between LBF and the basic basis function method are highlighted. The main difference lies in the approach to estimation. The primary version of the basis function method provides estimates for the entire analysis interval. The analysis window is then shifted so that estimates can be found for the next set of observations. In the case of the LBF method, the data from the analysis window are used to find parameter estimates for only one time instant within the analysis interval. The window is then moved to the subsequent observation and the estimation process is repeated. As a result, one obtains more accurate estimates at the expense of the increased computational burden.

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