Robust estimation in time series

A desirable property of an autocovariance estimator is to be robust to the presence of additive outliers. It is well-known that the sample autocovariance, based on the moments, does not own this property. Hence, the definition of an autocovariance estimator which is robust to additive outlier can be very useful for time-series modeling. In this paper, some asymptotic properties of the robust scale and autocovariance estimators proposed by Ma & Genton (2000) is study and applied to time series with different correlation structures. Introduction-References bases of this talk are: I FAJARDO M., F. A., REISEN, V. A., CRIBARI NETO, Francisco. Robust estimation in Long-memory processes under additive outliers. Journal of Statistical Planning and Inference, 139 , 2511 2525, 2009. I SARGNAGLIA, A. REISEN, V. A, C. LEVY-LEDUC. Robust estimation in PAR models in the presence of additive outliers, Journal of Multivariate Analysis, 2, 2168-2183, 2010. I C. LEVY-LEDUC. H. BOISTARD, MOULINES, E. M. S. TAQQU. and REISEN, V. A. Asymptotic properties of U-processes in long-range dependence. The Annals of Statistics, 39(3),1399-1246, 2011 I C. LEVY-LEDUC, H. BOISTARD, , MOULINES, E. MURAD S TAQQU and REISEN, V. A. Robust estimation of the scale and the autocovariance functions in short and long-range dependence. Journal of Time Series Analysis,32 (2),135-156. 2011. I LEVY-LEDUC, H. BOISTARD, MOULINES, E. MURAD S TAQQU and REISEN, V. A. Large sample behavior of some well-known robust estimators under long-range dependence,Statistics, 45(1),59-71, 2011. Applications: Nile river 622 1281 D.C. 622 722 822 922 1022 1122 1222 10 00 12 00 14 00 0 10 20 30 40 50 60 70 − 0. 1 0. 1 0. 3 0. 5