Ebook: Robust and Nonlinear Time Series Analysis: Proceedings of a Workshop Organized by the Sonderforschungsbereich 123 “Stochastische Mathematische Modelle”, Heidelberg 1983
- Tags: Statistics general
- Series: Lecture Notes in Statistics 26
- Year: 1984
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
Classical time series methods are based on the assumption that a particular stochastic process model generates the observed data. The, most commonly used assumption is that the data is a realization of a stationary Gaussian process. However, since the Gaussian assumption is a fairly stringent one, this assumption is frequently replaced by the weaker assumption that the process is wide~sense stationary and that only the mean and covariance sequence is specified. This approach of specifying the probabilistic behavior only up to "second order" has of course been extremely popular from a theoretical point of view be cause it has allowed one to treat a large variety of problems, such as prediction, filtering and smoothing, using the geometry of Hilbert spaces. While the literature abounds with a variety of optimal estimation results based on either the Gaussian assumption or the specification of second-order properties, time series workers have not always believed in the literal truth of either the Gaussian or second-order specifica tion. They have none-the-less stressed the importance of such optimali ty results, probably for two main reasons: First, the results come from a rich and very workable theory. Second, the researchers often relied on a vague belief in a kind of continuity principle according to which the results of time series inference would change only a small amount if the actual model deviated only a small amount from the assum ed model.
Content:
Front Matter....Pages N2-IX
On the Use of Bayesian Models in Time Series Analysis....Pages 1-16
Order Determination for Processes with Infinite Variance....Pages 17-25
Asymptotic Behaviour of the Estimates Based on Residual Autocovariances for ARMA Models....Pages 26-49
Parameter Estimation of Stationary Processes with Spectra Containing Strong Peaks....Pages 50-67
Linear Error-in-Variables Models....Pages 68-86
Minimax-Robust Filtering and Finite-Length Robust Predictors....Pages 87-126
The Problem of Unsuspected Serial Correlations....Pages 127-145
The Estimation of ARMA Processes....Pages 146-162
How to determine the bandwidth of some nonlinear smoothers in practice....Pages 163-184
Remarks on Nongaussian Linear Processes with Additive Gaussian Noise....Pages 185-197
Gross-Error Sensitivies of GM and RA-Estimates....Pages 198-217
Some Aspects of Qualitative Robustness in Time Series....Pages 218-230
Tightness of the Sequence of Empiric C.D.F. Processes Defined from Regression Fractiles....Pages 231-246
Robust Nonparametric Autoregression....Pages 247-255
Robust Regression by Means of S-Estimators....Pages 256-272
On Robust Estimation of Parameters for Autoregressive Moving Average Models....Pages 273-286
Back Matter....Pages 287-287
Content:
Front Matter....Pages N2-IX
On the Use of Bayesian Models in Time Series Analysis....Pages 1-16
Order Determination for Processes with Infinite Variance....Pages 17-25
Asymptotic Behaviour of the Estimates Based on Residual Autocovariances for ARMA Models....Pages 26-49
Parameter Estimation of Stationary Processes with Spectra Containing Strong Peaks....Pages 50-67
Linear Error-in-Variables Models....Pages 68-86
Minimax-Robust Filtering and Finite-Length Robust Predictors....Pages 87-126
The Problem of Unsuspected Serial Correlations....Pages 127-145
The Estimation of ARMA Processes....Pages 146-162
How to determine the bandwidth of some nonlinear smoothers in practice....Pages 163-184
Remarks on Nongaussian Linear Processes with Additive Gaussian Noise....Pages 185-197
Gross-Error Sensitivies of GM and RA-Estimates....Pages 198-217
Some Aspects of Qualitative Robustness in Time Series....Pages 218-230
Tightness of the Sequence of Empiric C.D.F. Processes Defined from Regression Fractiles....Pages 231-246
Robust Nonparametric Autoregression....Pages 247-255
Robust Regression by Means of S-Estimators....Pages 256-272
On Robust Estimation of Parameters for Autoregressive Moving Average Models....Pages 273-286
Back Matter....Pages 287-287
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