Unbiased Weighted Variance and Skewness Estimators for Overlapping Returns

This article develops unbiased weighted variance and skewness estimators for overlapping return distributions. These estimators extend the variance estimation methods constructed in Bod et. al. and Lo and MacKinlay. In addition, they may be used in overlapping return variance or skewness ratio tests as in Charles and Darné and Wong. An example using synthetic overlapping returns from a model fit to data from the SPY S&P 500 exchange traded fund is given in order to demonstrate under which circumstances the unbiased correction becomes significant in skewness estimation. Finally, we compare the effect of the HAC weighting schemes of Andrews as a function of sample size and overlapping return window length