Time Series Analysis: Forecasting and Control
The book is concerned with the building of models for discrete time series and dynamic systems. It describes in detail how such models may be used to obtain optimal forecasts and optimal control action. All the techniques are illustrated with examples using economic and industrial data. In Part 1, models for stationary and nonstationary time series are introduced, and their use in forecasting is discussed and exemplified. Part II is devoted to model building, and procedures for model identification, estimation, and checking which are then applied to the forecasting of seasonal time series. Part III is concerned with the building of transfer function models relating the input and output of a dynamic system computed by noise. In Part IV it is shown how transfer function and time series models may be used to design optimal feedback and feedforward control schemes. Part V contains an outline of computer programs useful in making the needed calculations and also includes charts and tables of value in identifying the models. (Author).
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INTRODUCTION AND SUMMARY
STOCHASTIC MODELS AND THEIR
LINEAR STATIONARY MODELS
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added adjustment appropriate approximate assumed autocorrelation function autocovariance calculated Chapter chart coefficients computed conditional consider constant continuous control scheme correlation corresponding cross defined derivatives described deviation difference equation discrete discussed distribution disturbance dynamic effect equal equation error estimates example expected expression Figure fitted fixed follows forecast forecast function given Hence identification illustration increase indicated initial input interval iteration lead least squares likelihood linear matrix mean moving average noise Normal observations obtained occur operator optimal origin output parameters particular period possible practice probability Program region represented residuals response roots sampling scheme shown shows squares standard stationary stochastic substituting sum of squares Suppose Table transfer function model unit values variable variance viscosity weights white noise write written zero