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

Joo-Mok Kim


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.


Self-Similar, Hurst parameter, FARIMA, Modified $R/S$ statistic, Power Spectrum Density

Subject classification

60G10, 60G18, 60G51.


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

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