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Robust estimation of (partial) autocorrelation

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Abstract The autocorrelation function (acf) and the partial autocorrelation function (pacf) are elementary tools of linear time series analysis. The sensitivity of the conventional sample acf and pacf to outliers is well known. We review robust estimators and evaluate their performances in different data situations considering Gaussian scenarios with and without outliers as well as times series with heavy tails in a simulation study. WIREs Comput Stat 2015, 7:205–222. doi: 10.1002/wics.1351 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Robust Methods Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data
Time series with 95% prediction bounds based on the univariate (left) and the bivariate (right) marginal distribution corresponding to subsequent observations. Univariate margins identify the most extreme observations as outliers, while multivariate inspection takes the dependencies between subsequent observations into account and identifies the true outliers.
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Efficiency under an outlier patch of length n0 = 0, 5, 10, 15, 20, 25 (from top to bottom in each panel) under a GARCH[0.05,0.85,0.1] model with n = 100 and a = 5.
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Efficiency (left) and bias (right) for a contaminated AR[0] model with n = 100 and outlier patches of length n0 = 0, 5, 10, 15, 20, 25 and a = 10.
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Efficiency (left) and bias (right) for a contaminated AR[0.8] model with n = 100 and n0 = 0, 5, 10, 15, 20, 25 (from top to bottom in each panel) isolated outliers and a = 20.
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Efficiency (left) and bias (right) for a contaminated AR[0.8] model with n = 100 and n0 = 0, 5, 10, 15, 20, 25 (from top to bottom in each panel) isolated outliers and a = 5.
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Simulated bias of a contaminated AR[0] model with n = 100 and a patch of 5 (left) or 20 outliers (right).
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Efficiency (left) and bias (right) for n = 50, 100, 500 (from top to bottom in each panel) for an AR[0.4] model with normal innovations.
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Autocorrelation functions of the processes considered in the simulations.
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Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data
Statistical and Graphical Methods of Data Analysis > Robust Methods

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