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).
STOCHASTIC MODELS AND THEIR
LINEAR STATIONARY MODELS
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a₁ Appendix approximate ARMA autocorrelation function autocovariance autoregressive operator autoregressive process behavior calculation Chapter coefficients computed conditional expectations consider contours correlation function covariance cross correlation cross correlation function cross covariance deviations diagnostic checking difference equation differencing discrete distribution estimated autocorrelations example exponentially first-order fitted forecast errors given Hence identification impulse response initial estimates input interval invertibility iteration Lags large samples lead least squares estimates likelihood function linear matrix mean square error minimum mean square moving average process n₁ nonstationary Normal observations obtained optimal output p₁ parameters partial autocorrelation partial autocorrelation function particular periodogram process of order quadratic recursion residuals second-order Section shows square error forecast standard error starting values stationary stationary process stochastic model substituting sum of squares Suppose Table transfer function model V²z variance w₁ weights white noise X₁ Y₁ Z₁ zero Φι