Time Series: Theory and Methods

1. Front Matter

   Pages i-xiv

   PDF

2. Stationary Time Series

   • Peter J. Brockwell, Richard A. Davis

   Pages 1-41

3. Hilbert Spaces

   • Peter J. Brockwell, Richard A. Davis

   Pages 42-76

4. Stationary ARMA Processes

   • Peter J. Brockwell, Richard A. Davis

   Pages 77-111

5. The Spectral Representation of a Stationary Process

   • Peter J. Brockwell, Richard A. Davis

   Pages 112-158

6. Prediction of Stationary Processes

   • Peter J. Brockwell, Richard A. Davis

   Pages 159-190

7. Asymptotic Theory

   • Peter J. Brockwell, Richard A. Davis

   Pages 191-210

8. Estimation of the Mean and the Autocovariance Function

   • Peter J. Brockwell, Richard A. Davis

   Pages 211-230

9. Estimation for ARMA Models

   • Peter J. Brockwell, Richard A. Davis

   Pages 231-264

10. Model Building and Forecasting with ARIMA Processes

    • Peter J. Brockwell, Richard A. Davis

    Pages 265-319

11. Inference for the Spectrum of a Stationary Process

    • Peter J. Brockwell, Richard A. Davis

    Pages 320-390

12. Multivariate Time Series

    • Peter J. Brockwell, Richard A. Davis

    Pages 391-446

13. Further Topics

    • Peter J. Brockwell, Richard A. Davis

    Pages 447-498

14. Back Matter

    Pages 499-519

    PDF

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.

• estimator
• likelihood
• statistics
• time series

• Department of Statistics, Colorado State University, Fort Collins, USA

  Peter J. Brockwell, Richard A. Davis

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