Robust and Nonlinear Time Series Analysis

1. Front Matter

   Pages N2-IX

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2. On the Use of Bayesian Models in Time Series Analysis

   • Hirotugu Akaike

   Pages 1-16

3. Order Determination for Processes with Infinite Variance

   • R. J. Bhansali

   Pages 17-25

4. Asymptotic Behaviour of the Estimates Based on Residual Autocovariances for ARMA Models

   • Oscar Bustos, Ricardo Fraiman, Victor J. Yohai

   Pages 26-49

5. Parameter Estimation of Stationary Processes with Spectra Containing Strong Peaks

   • Rainer Dahlhaus

   Pages 50-67

6. Linear Error-in-Variables Models

   • M. Deistler

   Pages 68-86

7. Minimax-Robust Filtering and Finite-Length Robust Predictors

   • Jürgen Franke, H. Vincent Poor

   Pages 87-126

8. The Problem of Unsuspected Serial Correlations

   • H. Graf, F. R. Hampel, J.-D. Tacier

   Pages 127-145

9. The Estimation of ARMA Processes

   • E. J. Hannan

   Pages 146-162

10. How to determine the bandwidth of some nonlinear smoothers in practice

    • Wolfgang Härdle

    Pages 163-184

11. Remarks on Nongaussian Linear Processes with Additive Gaussian Noise

    • K. S. Lii, M. Rosenblatt

    Pages 185-197

12. Gross-Error Sensitivies of GM and RA-Estimates

    • R. Douglas Martin, V. J. Yohai

    Pages 198-217

13. Some Aspects of Qualitative Robustness in Time Series

    • P. Papantoni-Kazakos

    Pages 218-230

14. Tightness of the Sequence of Empiric C.D.F. Processes Defined from Regression Fractiles

    • Stephen Portnoy

    Pages 231-246

15. Robust Nonparametric Autoregression

    • P. M. Robinson

    Pages 247-255

16. Robust Regression by Means of S-Estimators

    • P. Rousseeuw, V. Yohai

    Pages 256-272

17. On Robust Estimation of Parameters for Autoregressive Moving Average Models

    • Pham Dinh Tuan

    Pages 273-286

18. Back Matter

    Pages 287-287

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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.

• Analysis
• Estimator
• Series
• Time
• Time series
• Variance
• correlation

• Fachbereich Mathematik, Universität Frankfurt, Frankfurt, Germany

  Jürgen Franke, Wolfgang Härdle

• Department of Statistics, GN-22, University of Washington, Seattle, USA

  Douglas Martin

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