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Abstract:
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When the correlation between current and lagged observations decays very slowly, data collected over time often have the property of long memory, which has been characterized in various ways in the literature. Perhaps the four most popular characterizations of long memory are based on the autocorrelation function, on the self-similarity index, on ARFIMA-type models and on the Hurst exponent. In this paper, we investigate relationships between those four approaches and derive some of their properties. Further, we focus on several estimators of long memory and via simulation estimate the bias, sampling standard deviation and root mean squared error under a set of true values of the Hurst exponent. Finally, we compare the performance of several estimators of Hurst exponent by applying them to a subset of the S&P 500 series and without relying on an underlying dynamic model.
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