Time Series

This book includes contributions from researchers, scholars, and professionals about the most recent theory, models, and applications for interdisciplinary and multidisciplinary research encircling disciplines of computer science, mathematics, statistics, geography, and more in time series analysis and forecasting/backcasting.

Time series consist of data observed sequentially in time, and they are assumed to stem from an underlying stochastic process. The scope of time series approaches thus covers models for stochastic processes as well as inferential procedures for model fitting, model diagnostics, forecasting, and various other applications.

This book includes contributions from researchers, scholars, and professionals about the most recent theory, models, and applications for interdisciplinary and multidisciplinary research encircling disciplines of computer science, mathematics, statistics, geography, and more in time series analysis and forecasting/backcasting.

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Books on time series models deal mainly with models based on Box-Jenkins methodology which is generally represented by autoregressive integrated moving average models or some nonlinear extensions of these models, such as generalized autoregressive conditional heteroscedasticity models. Statistical inference for these models is well developed and commonly used in practical applications, due also to statistical packages containing time series analysis parts. The present book is based on regression models used for time series. These models are used not only for modeling mean values of observed time se­ ries, but also for modeling their covariance functions which are often given parametrically. Thus for a given finite length observation of a time series we can write the regression model in which the mean value vectors depend on regression parameters and the covariance matrices of the observation depend on variance-covariance parameters. Both these dependences can be linear or nonlinear. The aim of this book is to give an unified approach to the solution of statistical problems for such time series models, and mainly to problems of the estimation of unknown parameters of models and to problems of the prediction of time series modeled by regression models.

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.