Robust estimation of AR coefficients under simultaneously influencing outliers and missing values |
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Authors: | Yuriy S. Kharin Valeriy A. Voloshko |
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Affiliation: | Department of Mathematical Modeling and Data Analysis, Belarusian State University, 4 Independence Avenue, Minsk 220030, Belarus |
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Abstract: | A family of robust estimators for coefficients of Gaussian AR(p) time series under simultaneously influencing distortions of two types: outliers and missing values, is proposed. The estimators are based on special properties of the Cauchy probability distribution; consistency and the asymptotic normality of these estimators are proven. An approximate solution of the problem of minimization of the asymptotic variance within the proposed family of estimators is found. Performance of the proposed estimators is illustrated for simulated time series and for real data sets. |
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Keywords: | Outlier Missing value Robust estimator Time series Autoregression Cauchy distribution |
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