Journal of Statistics: Advances in Theory and ApplicationsAuthor's: Erhard Reschenhofer
Pages: [45] - [54]
Received Date: August 23, 2017
Submitted by:
DOI: http://dx.doi.org/10.18642/jsata_7100121869
This paper investigates some theoretical properties of a simple estimator for the location parameter of a Cauchy distribution and a truncated Cauchy distribution, respectively, which can also be used for the robust estimation of the first-order autocorrelation of a stationary time series. Because of its simplicity and its robustness against heteroscedasticity and extreme values, this estimator is particularly useful for the analysis of serial correlation in financial time series. When applied to suitably transformed observations from a Cauchy distribution, this estimator is more efficient than competing estimators such as the sample median, trimmed means and other estimators based on sample order statistics.
truncated Cauchy distribution, sample median, bias, Cramer-Rao lower bound.
