Time Series : Theory and Methods

Time Series: Theory and Methods is a systematic account of linear time series models and their application to the modelling and prediction of data collected sequentially in time. The aim is to provide specific techniques for handling data and at the same time to provide a thorough understanding of the mathematical basis for techniques. Both time and frequency domain methods are discussed but the book is written in such a way that either approach could be emphasized. It is intended to be a text for graduate students in statistics, mathematics, engineering, and the natural or social sciences. It contains substantial chapters on multivariate series and state-space models (including applications of the Kalman recursions to missing-value problems) and shorter accounts of special topics including long-range dependence, infinite variance processes and non-linear models. It can be used either at the MS level, emphasizing the more practical aspects of modelling, or at the PhD level, where the detailed mathematical derivations of the deeper results can be included. Distinctive features of the book are the extensive use of elementary Hilbert space methods and recursive prediction techniques based on innovations, use of the exact Gaussian likelihood and AIC for inference, a thorough treatment of the asymptotic behaviour of the maximum likelihood estimators of the coefficients of univariate ARMA models, extensive illustrations of the techniques by means of numerical examples, and a large number of problems for the reader. The companion software package (ITSM), which is available with the manual, "ITSM: Interactive Time Series Modelling Programs for the PC", contains a variety of interactive time series modelling and forecasting programs written for the IBM PC and compatible computers. These can be used to apply the methods described in the text to the data sets supplied, to simulated data sets (which can be generated by one of the programs provided) or to data provided by the reader. "Along with its excellent exposition, there are many features of this book that make it attractive as a textbook or reference. well organized and clearly written. extremely useful. self-contained." #Journal of The American Statistical Association#1