In this paper we define subset bilinear time series models, and then describe an algorithm for the estimation of these models. It is also pointed out that for this class of non-linear time series models, it is possible to obtain optimal several step predictors. The estimation technique of these models is illustrated with respect to three time series, and the optimal several steps ahead forecasts of these time series models are calculated. A comparison of these forecasts is made with the forecasts obtained by the best linear autoregressive and threshold autoregressive models. The residuals obtained from the models are tested for independence and Gaussianity using higher order moments.
A standard assumption that is often made in time series analysis is that the series conforms to a linear model. The object of this paper is to describe statistical tests for testing this assumption. The tests are constructed from the bispectral density function, and depend on the application of Hotelling T 2 . These tests are illustrated with two real time series and four simulated time series. Some guidelines about the choice of the parameters are also included.
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