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Multiple Time Series by E. J. Hannan
English | PDF | 1970 | 542 Pages | ISBN : 0471348058 | 21.8 MB
The subject of time series analysis has intimate connections with a wide range of topics, among which may be named statistical communication theory, the theory of prediction and control, and the statistical analysis of time series data. The last of these is to some extent subsidiary to the other two, since its purpose, in part at least, must be to provide the information essential to the application of those theories. However, it also has an existence of its own because of its need in fields (e.g., economics) in which at present well-developed, exact theories of control are not possible.
The subject of time series analysis has intimate connections with a wide range of topics, among which may be named statistical communication theory, the theory of prediction and control, and the statistical analysis of time series data. The last of these is to some extent subsidiary to the other two, since its purpose, in part at least, must be to provide the information essential to the application of those theories. However, it also has an existence of its own because of its need in fields (e.g., economics) in which at present well-developed, exact theories of control are not possible.
It is with the third of these topics that this book is concerned. It extends beyond that in two ways. The first and most important is by the inclusion in the first half of the book of a fairly complete treatment of the underlying probability theory for second-order stationary process. Although this theory is for the most part classical and available elsewhere in book form, its understanding is an essential preliminary to the study of time series analysis and its inclusion is inevitable. I have, however, included a certain amount of material over and above the minimum necessary, in relation, for example, to nonlinear filters and random processes in space as well as time. The statistical development of this last subject is now fragmentary but may soon become important. The second additional topic is the theory of prediction, interpolation, signal extraction, and smoothing of time series. The inclusion of this material seems justified for two reasons. The first arises from the understanding that the classical "Wiener-Kolmogoroff" theories give of the structure of time series. This understanding is needed, in part at least, for statistical developments (e.g., identification problems and problems associated with the relation between the eigenvalues of the covariance matrix and the spectrum). The second reason is that these developments are becoming important to people who are statisticians concerned with time series (e.g., in missile trajectory estimation and economics). Of course, some of the more practically valuable work here is recent and would require a separate volume for an adequate treatment, but some indications concerning it are needed. There is one other characteristic that a modern book on time series must have and that is the development of the theory and methods for the case in which multiple measurements are made at each point, for this is usually the case.
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