Title | Robust and Nonlinear Time Series Analysis [electronic resource] : Proceedings of a Workshop Organized by the Sonderforschungsbereich 123 "Stochastische Mathematische Modelle", Heidelberg 1983 / edited by Jรผrgen Franke, Wolfgang Hรคrdle, Douglas Martin |
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Imprint | New York, NY : Springer US, 1984 |

Connect to | http://dx.doi.org/10.1007/978-1-4615-7821-5 |

Descript | 286 p. online resource |

SUMMARY

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 widẽsense 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 beยญ 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 specificaยญ tion. They have none-the-less stressed the importance of such optimaliยญ 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 assumยญ ed model

CONTENT

On the Use of Bayesian Models in Time Series Analysis -- Order Determination for Processes with Infinite Variance -- Asymptotic Behaviour of the Estimates Based on Residual Autocovariances for ARMA Models -- Parameter Estimation of Stationary Processes with Spectra Containing Strong Peaks -- Linear Error-in-Variables Models -- Minimax-Robust Filtering and Finite-Length Robust Predictors -- The Problem of Unsuspected Serial Correlations -- The Estimation of ARMA Processes -- How to Determine the Bandwidth of some Nonlinear Smoothers in Practice -- Remarks on NonGaussian Linear Processes with Additive Gaussian Noise -- Gross-Error Sensitivies of GM and RA-Estimates -- Some Aspects of Qualitative Robustness in Time Series -- Tightness of the Sequence of Empiric C.D.F. Processes Defined from Regression Fractiles -- Robust Nonparametric Autoregression -- Robust Regression by Means of S-Estimators -- On Robust Estimation of Parameters for Autoregressive Moving Average Models

Mathematics
Applied mathematics
Engineering mathematics
Probabilities
Mathematics
Probability Theory and Stochastic Processes
Applications of Mathematics