Simultaneous estimation of the parameters of the Hurst-Kolmogorov stochastic process

Tyralis, H; Koutsoyiannis, D

dc.contributor.author	Tyralis, H	en
dc.contributor.author	Koutsoyiannis, D	en
dc.date.accessioned	2014-03-01T01:37:05Z
dc.date.available	2014-03-01T01:37:05Z
dc.date.issued	2011	en
dc.identifier.issn	14363240	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/21440
dc.subject	Hurst parameter estimators	en
dc.subject	Hurst phenomenon	en
dc.subject	Hurst-Kolmogorov behaviour	en
dc.subject	Hydrological estimation	en
dc.subject	Hydrological statistics	en
dc.subject	Long term persistence	en
dc.subject.other	Hurst parameter	en
dc.subject.other	Hurst phenomenon	en
dc.subject.other	Hydrological estimation	en
dc.subject.other	Hydrological statistics	en
dc.subject.other	Kolmogorov	en
dc.subject.other	Long term	en
dc.subject.other	Computational complexity	en
dc.subject.other	Maximum likelihood estimation	en
dc.subject.other	Random processes	en
dc.subject.other	Stochastic systems	en
dc.subject.other	Time series	en
dc.subject.other	Parameter estimation	en
dc.subject.other	computer simulation	en
dc.subject.other	estimation method	en
dc.subject.other	hydrology	en
dc.subject.other	least squares method	en
dc.subject.other	maximum likelihood analysis	en
dc.subject.other	numerical model	en
dc.subject.other	parameterization	en
dc.subject.other	performance assessment	en
dc.subject.other	stochasticity	en
dc.subject.other	time series analysis	en
dc.title	Simultaneous estimation of the parameters of the Hurst-Kolmogorov stochastic process	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00477-010-0408-x	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00477-010-0408-x	en
heal.publicationDate	2011	en
heal.abstract	Various methods for estimating the self-similarity parameter (Hurst parameter, H) of a Hurst-Kolmogorov stochastic process (HKp) from a time series are available. Most of them rely on some asymptotic properties of processes with Hurst-Kolmogorov behaviour and only estimate the self-similarity parameter. Here we show that the estimation of the Hurst parameter affects the estimation of the standard deviation, a fact that was not given appropriate attention in the literature. We propose the least squares based on variance estimator, and we investigate numerically its performance, which we compare to the least squares based on standard deviation estimator, as well as the maximum likelihood estimator after appropriate streamlining of the latter. These three estimators rely on the structure of the HKp and estimate simultaneously its Hurst parameter and standard deviation. In addition, we test the performance of the three methods for a range of sample sizes and H values, through a simulation study and we compare it with other estimators of the literature. © 2010 Springer-Verlag.	en
heal.journalName	Stochastic Environmental Research and Risk Assessment	en
dc.identifier.doi	10.1007/s00477-010-0408-x	en
dc.identifier.volume	25	en
dc.identifier.issue	1	en
dc.identifier.spage	21	en
dc.identifier.epage	33	en