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Estimation of the local Hurst function of multifractional Brownian motion: A second difference increment ratio estimator
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2015 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

In this thesis, a specific type of stochastic processes displaying time-dependent regularity is studied. Specifically, multifractional Brownian motion processes are examined. Due to their properties, these processes have gained interest in various fields of research. An important aspect when modeling using such processes are accurate estimates of the time-varying pointwise regularity. This thesis proposes a moving window ratio estimator using the distributional properties of the second difference increments of a discretized multifractional Brownian motion. The estimator captures the behaviour of the regularity on average. In an attempt to increase the accuracy of single trajectory pointwise estimates, a smoothing approach using nonlinear regression is employed. The proposed estimator is compared to an estimator based on the Increment Ratio Statistic.

Abstract [sv]

I denna uppsats studeras en specifik typ av stokastiska processer, vilka uppvisar tidsberoende regelbundenhet. Specifikt behandlas multifraktionella Brownianska rörelser då deras egenskaper föranlett ett ökat forskningsintresse inom flera fält. Vid modellering med sådana processer är noggranna estimat av den punktvisa, tidsberoende regelbundenheten viktig. Genom att använda de distributionella egenskaperna av andra ordningens inkrement i ett rörligt fönster, är det möjligt att skatta den punktvisa regelbundenheten av en sådan process. Den föreslagna estimatorn uppnår i genomsnitt precisa resultat. Dock observeras hög varians i de punktvisa estimaten av enskilda trajektorier. Ickelinjär regression appliceras i ett försök att minska variansen i dessa estimat. Vidare presenteras ytterligare en estimator i utvärderingssyfte.

Place, publisher, year, edition, pages
2015. , 32 p.
National Category
URN: urn:nbn:se:umu:diva-105770OAI: diva2:828116
Available from: 2015-11-04 Created: 2015-06-29 Last updated: 2015-11-04Bibliographically approved

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