Korean J. Math. Vol. 26 No. 2 (2018) pp.155-166
DOI: https://doi.org/10.11568/kjm.2018.26.2.155

Estimation of hurst parameter and minimum variance spectrum

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Published: Jun 30, 2018
Keywords:
Self-Similar, Hurst parameter, FARIMA, Modified $R/S$ statistic, Power Spectrum Density
Mathematics Subject Classification:
60G10, 60G18, 60G51.

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Joo-Mok Kim
School of General Education Semyung University Jecheon 27136, Korea

Abstract

Consider FARIMA time series with innovations that have infinite variances. We are interested in the estimation of self-similarities $H_n$ of FARIMA$(0, d, 0)$ by using modified $R/S$ statistic. We can confirm that the $H_n$ converges to Hurst parameter $H=d+\frac12$. Finally, we figure out ARMA and minimum variance power spectrum density of FARIMA processes.


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Supporting Agencies

This work was supported by Semyung University Research Grant in 2016.

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