Predictions in Time Series Using Regression Models

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Springer Science & Business Media, Apr 12, 2002 - Mathematics - 233 pages
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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.
 

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Contents

Hilbert Spaces and Statistics
1
12 Preliminaries from Statistics
6
13 Estimation of Parameters
12
14 Double Least Squares Estimators
24
15 Invariant Quadratic Estimators
30
16 Unbiased Invariant Estimators
37
Random Processes and Time Series
51
22 Models for Random Processes
53
34 Maximum Likelihood Estimation
118
Predictions of Time Series
147
42 Predictions in Linear Models
149
43 Model Choice and Predictions
165
44 Predictions in Multivariate Models
179
45 Predictions in Nonlinear Models
189
Empirical Predictors
197
52 Properties of Empirical Predictors
198

23 Spectral Theory
61
24 Models for Time Series
65
Estimation of Time Series Parameter
73
32 Estimation of Mean Value Parameters
74
33 Estimation of a Covariance Function
99
53 Numerical Examples
208
References
223
Index
229
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