On the robust estimation of autocorrelations in the presence of outliers and shifts

• Department of Statistics, TU Dortmund University, Dortmund, Germany [fried@statistik.tu-dortmund.de, gierse@statistik.tu-dortmund.de]

Keywords: Time series analysis – Change-points – Robustness

1 General Information

Autocorrelation functions are basic measures of linear dependence in time series analysis and spatial statistics under the assumption of second order stationarity. Popular estimators of these characteristics are strongly affected by outliers and level shifts, whereas methods for detection of such deviations from the underlying stationarity assumptions require reliable estimates of these second order characteristics.

We explore several kinds of robust autocorrelation estimators in this context, which are constructed using different principles. The use of the minimum covariance determinant estimator has been discussed by Dürre et al. (2015). Robust estimators which tolerate a certain fraction of level shifts in the data can be constructed from partitionings of the data into different blocks, in a similar vein as the robust scale estimators designed by Axt et al. (2021). Correcting the data for the most plausible shift has been suggested e.g. by Huskova and Kirch (2008). A robust autocorrelation estimator under Gaussian assumptions can be derived from the medians of pairwise differences at different time lags, see Chakar et al.(2017).

We investigate the asymptotic consistency and the breakdown behaviour of the arising estimators, and we evaluate the finite sample performance of the different methods by simulations in several data scenarios with outliers and level shifts. The usefulness of the proposals is illustrated by real data applications including e.g. satellite data from Landsat 8.