Highly Robust Estimation of the Autocovariance Function

Abstract

In this paper, the problem of the robustness of the sample autocovariance function is addressed. We propose a new autocovariance estimator, based on a highly robust estimator of scale. Its robustness properties are studied by means of the in¯uence function, and a new concept of temporal breakdown point. As the theoretical variance of the estimator does not have a closed form, we perform a simulation study. Situations with various size of outliers are tested. They con®rm the robustness properties of the new estimator. An S-Plus function for the highly robust autocovariance estimator is made available on the Web at http://www-math.mit.edu/ $ yanyuan/Genton/Time/time.html. At the end, we analyze a time series of monthly interest rates of an Austrian bank.

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