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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to Journal of the American Statistical Association.Autoregressive models for spatial interaction have been proposed by several authors (Whittle [15] and Mead [11], for example). In the past, computational difficulties with the ML approach have led to the use of alternative estimators. In this article, a simplified computational scheme is given and extended to mixed regressive-autoregressive models. The ML estimator is compared with several alternatives.

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A class of dynamic, nonlinear, statistical models is introduced for the analysis of univariate time series. A distinguishing feature of the models is their reliance on only one primary source of randomness: a sequence of independent and identically distributed normal disturbances. It is established that the models are conditionally Gaussian. This fact is used to define a conditional maximum likelihood method of estimation and prediction. A particular member of the class is shown to provide the statistical foundations for the multiplicative Holt-Winters method of forecasting. This knowledge is exploited to provide methods for computing prediction intervals to accompany the more usual point predictions obtained from the Holt-Winters method. The methods of estimation and prediction are evaluated by simulation. They are also illustrated with an application to Canadian retail sales.

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