Time Series : Theory and Methods
This study gives an 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 instill an understanding of the mathematical basis behind these techniques. The text contains 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. 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, treatment of the asymptotic behaviour of the maximum likelihood estimators of the coefficients of univariate ARMA models, illustrations of the techniques by means of numerical examples, and a number of problems for the reader.
- Hardback | 593 pages
- 138 x 216mm | 975g
- 01 Mar 1991
- Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
- Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Berlin, Germany
- 2nd Revised edition
Table of contents
Stationary Time Series.- Hilbert Spaces.- Stationary ARMA Processes.- The Spectral Representation of a Stationary Process.- Prediction of Stationary Processes.- Asymptotic Theory.- Estimation of the Mean and the Autocovariance Function.- Estimation for ARMA Models.- Model Building and Forecasting with ARIMA Processes.- Inference for the Spectrum of a Stationary Process.- Multivariate Time Series.- State-Space Models and the Kalman Recursions.- Further Topics.- Appendix: Data Sets.- Bibliography.- Index.