Until recently the models considered for time series have usually been linear with constant coefficients. In most situations one would not expect such models to be the “best” class of model to fit to a set of real data, although one tacitly makes the assumption that the linear model under consideration is a close approximation to physical reality. A number of factors have resulted in a consideration of different classes of non-linear models, not the least of which is that the theory of linear models is essentially complete. A large amount of the research into these models is now being concentrated on the construction and application of computationally efficient algorithms to determine order and obtain estimates of the unknown parameters which have desirable statistical properties. The increased power and speed of modern computers has also had a significant effect on the direction in which time series research has headed. This is clearly demonstrated for example by the computational requirements of Akaike’s criterion (see Akaike (1978)) to determine the order of a particular linear time series model. With the increase in computer capabilities the application of such criteria has become routine.
KeywordsAutoregressive Model Vary Parameter Model Martingale Central Limit Theorem Linear Time Series Model Time Vary Parameter Model
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