Time Series: Theory and Methods

Front Cover
Springer Science & Business Media, Nov 11, 2013 - Mathematics - 520 pages
We have attempted in this book to give 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 the techniques. Both time and frequency domain methods are discussed but the book is written in such a way that either approach could be emphasized. The book is intended to be a text for graduate students in statistics, mathematics, engineering, and the natural or social sciences. It has been used both at the M. S. level, emphasizing the more practical aspects of modelling, and at the Ph. D. 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 behavior of the maximum likelihood estimators of the coefficients of univariate ARMA models, extensive illustrations of the tech niques by means of numerical examples, and a large number of problems for the reader. The companion diskette contains programs written for the IBM PC, which can be used to apply the methods described in the text.
 

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Contents

CHAPTER
19
CHAPTER 3
25
CHAPTER 2
42
29 Hilbert Space Isomorphisms
67
Stationary ARMA Processes
77
CHAPTER 4
112
44 Spectral Densities and ARMA Processes
120
49 Inversion Formulae
145
CHAPTER 9
265
CHAPTER 10
320
103 Asymptotic Properties of the Periodogram
332
CHAPTER 11
391
6 The Cross Spectrum
419
CHAPTER 12
447
122 Transfer Function Modelling
454
124 Long Memory Processes
464

CHAPTER 5
159
CHAPTER
191
Estimation of the Mean and the Autocovariance Function
211
CHAPTER 8
231
Data Sets
499
Index
509
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