On Estimation of Hurst Parameter Under Noisy Observations

Guangying Liu and Bing-Yi Jing

Journal of Business & Economic Statistics, 2018, vol. 36, issue 3, 483-492

Abstract: It is widely accepted that some financial data exhibit long memory or long dependence, and that the observed data usually possess noise. In the continuous time situation, the factional Brownian motion BH and its extension are an important class of models to characterize the long memory or short memory of data, and Hurst parameter H is an index to describe the degree of dependence. In this article, we estimate the Hurst parameter of a discretely sampled fractional integral process corrupted by noise. We use the preaverage method to diminish the impact of noise, employ the filter method to exclude the strong dependence, and obtain the smoothed data, and estimate the Hurst parameter by the smoothed data. The asymptotic properties such as consistency and asymptotic normality of the estimator are established. Simulations for evaluating the performance of the estimator are conducted. Supplementary materials for this article are available online.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlbes:v:36:y:2018:i:3:p:483-492

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DOI: 10.1080/07350015.2016.1191503

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