Hurt, Jan; Kuhlisch, Wiltrud A simple robust estimator of correlations for Gaussian stationary random sequences. (English) Zbl 0857.62084 Kybernetika 31, No. 5, 481-488 (1995). Summary: The paper deals with a robust estimation of correlations for a Gaussian stationary sequence. The investigated estimator is based on signs of the original series and is easy to compute. The asymptotic normality of the estimator and the boundedness of the influence functional under the assumption of the pure replacement outlier model have been proved. A consistent estimate of the variance of the asymptotic distribution has been sugested. MSC: 62M09 Non-Markovian processes: estimation 62F35 Robustness and adaptive procedures (parametric inference) 62F12 Asymptotic properties of parametric estimators Keywords:robust estimation of correlations; Gaussian stationary sequence; asymptotic normality; pure replacement outlier model; consistent estimate; asymptotic distribution PDFBibTeX XMLCite \textit{J. Hurt} and \textit{W. Kuhlisch}, Kybernetika 31, No. 5, 481--488 (1995; Zbl 0857.62084) Full Text: EuDML Link References: [1] M. Fisz: Wahrscheinlichkeitsrechnung und Mathematische Statistik. Akademie-Verlag, Berlin 1970. · Zbl 0216.46101 [2] J. Hurt: On a simple estimate of correlations of stationary random sequences. Apl. Mat. 18 (1973), 176-187. · Zbl 0265.62032 [3] B. Kedem: Binary Time Series. M. Dekker, New York 1980. · Zbl 0424.62062 [4] R. D. Martin, V. J. Yohai: Robustness in time series and estimating ARMA models. Handbook of Statistics 5, Time Series in the Time Domain (E. J. Hannan, P. R. Krishnaih, and M. M. Rao, Elsevier, Amsterdam 1985, pp. 119-155. [5] R. D. Martin, V. J. Yohai: Influence functionals for time series. Ann. Statist. 14 (1986), 781-818. · Zbl 0608.62042 · doi:10.1214/aos/1176350027 [6] C. R. Rao: Linear Statistical Inference and Its Applications. Wiley, New York 1965. · Zbl 0137.36203 [7] W. F. Stout: Almost Sure Convergence. Academic Press, New York 1974. · Zbl 0321.60022 [8] N. M. Sujev: Investigation of spectral densities of mixing random processes. Dokl. Akad. Nauk 507 (1972), 773-776. In Russian. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.