Journal ArticleDOI
Estimators based on ranks for arma models
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In this paper, a new family of robust estimators for ARMA models is defined by replacing the residual sample autocovariances in the least squares equations by autoc covariances based on ranks.Abstract:
In this paper we introduce a new family of robust estimators for ARMA models. These estimators are defined by replacing the residual sample autocovariances in the least squares equations by autocovariances based on ranks. The asymptotic normality of the proposed estimators is provided. The efficiency and robustness properties of these estimators are studied. An adequate choice of the score functions gives estimators which have high efficiency under normality and robustness in the presence of outliers. The score functions can also be chosen so that the resulting estimators are asymptotically as efficient as the maximum likelihood estimators for a given distribution.read more
Citations
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Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
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Linear serial rank tests for randomness against ARMA alternatives
TL;DR: In this paper, a class of linear serial rank statistics for the problem of testing white noise against alternatives of ARMA serial dependence is introduced, and the efficiency properties of the proposed statistics are investigated, and an explicit formulation of the asymptotically most efficient score-generating functions is provided.
Journal ArticleDOI
Robust estimation of (partial) autocorrelation
TL;DR: In this paper, robust estimators and their performance in different data situations considering Gaussian scenarios with and without outliers as well as times series with heavy tails in a simulation study are evaluated.
Journal ArticleDOI
Rank-Based Estimation for Autoregressive Moving Average Time Series Models
TL;DR: In this article, rank-based estimators of autoregressive-moving average model parameters are obtained by minimizing a rankbased residual dispersion function similar to the one given by L.A. Jaeckel, which can have the same asymptotic efficiency as maximum likelihood estimators and are robust.
Journal ArticleDOI
Theory & Methods: Weighted Wilcoxon Estimates for Autoregression
TL;DR: In this paper, the authors explore the class of weighted Wilcoxon (WW) estimates in the context of autoregressive parameter estimation, giving special attention to three sub-classes of so-called WW-estimates.
References
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Time series analysis, forecasting and control
TL;DR: In this article, a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970 is presented, focusing on practical techniques throughout, rather than a rigorous mathematical treatment of the subject.
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Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
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TL;DR: Numerical Recipes: The Art of Scientific Computing as discussed by the authors is a complete text and reference book on scientific computing with over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, with many new topics presented at the same accessible level.
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Time Series Analysis Forecasting and Control
TL;DR: This revision of a classic, seminal, and authoritative book explores the building of stochastic models for time series and their use in important areas of application forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control.