A New Clipping Approach for Robust ACF Estimation

Anotace: The importance of working with sufficiently robust methods has been rising in recent years. This growth is related to the extensive usage of highly frequent data, which we currently encounter in many fields including finance. Since with an increasing number of observations, the probability of outlier presence also rises. Moreover, as it is known, standard methods are not able to work correctly with outliers and, consequently, standard estimates are often biased. We focus on estimators of autocorrelation function for univariate time series, for which we propose a method based on clipping an original time series and working with a binary time series instead. The clipping helps to deal with outliers and the estimation is not affected as much as with standard methods. We also derive an asymptotical distribution of the estimator, what gives our method a major advantage in comparison with other robust methods, which are often presented without this. Furthermore, knowing the distribution of the estimator allows us to perform statistical inference.