Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Estimation of the Hurst parameter for fractional Brownian motion using the CMARS method
Date
2014-03-15
Author
Yerlikaya-Ozkurt, F.
Vardar Acar, Ceren
Yolcu-Okur, Y.
Weber, G. -W.
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
259
views
0
downloads
Cite This
In this study, we develop an alternative method for estimating the Hurst parameter using the conic multivariate adaptive regression splines (CMARS) method. We concentrate on the strong solutions of stochastic differential equations (SDEs) driven by fractional Brownian motion (fBm). Our approach is superior to others in that it not only estimates the Hurst parameter but also finds spline parameters of the stochastic process in an adaptive way. We examine the performance of our estimations using simulated test data.
Subject Keywords
Stochastic differential equations
,
Fractional Brownian motion
,
Hurst parameter
,
Conic multivariate adaptive regression splines
URI
https://hdl.handle.net/11511/40852
Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
DOI
https://doi.org/10.1016/j.cam.2013.08.001
Collections
Department of Statistics, Article
Suggestions
OpenMETU
Core
EVALUATING THE CMARS PERFORMANCE FOR MODELING NONLINEARITIES
Batmaz, İnci; Kartal-Koc, Elcin; Köksal, Gülser (2010-02-04)
Multivariate Adaptive Regression Splines (MARS) is a very popular nonparametric regression method particularly useful for modeling nonlinear relationships that may exist among the variables. Recently, we developed CMARS method as an alternative to backward stepwise part of the MARS algorithm. Comparative studies have indicated that CMARS performs better than MARS for modeling nonlinear relationships. In those studies, however, only main and two-factor interaction effects were sufficient to model the nonline...
Refinements, extensions and modern applications of conic multivariate adaptive regression splines
Yerlikaya Özkurt, Fatma; Weber, Gerhard Wilhelm; Department of Scientific Computing (2013)
Conic Multivariate Adaptive Regression Splines (CMARS) which has been developed at the Institute of Applied Mathematics, METU, as an alternative approach to the well-known data mining tool Multivariate Adaptive Regression Splines (MARS). CMARS is based on given data and a penalized residual sum of squares for MARS, interpreted as a Tikhonov Regularization problem. CMARS treats this problem by a continuous optimization technique called Conic Quadratic Programming (CQP). This doctoral thesis adapts the CMARS ...
CMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization
Weber, Gerhard-Wilhelm; Batmaz, İnci; Köksal, Gülser; Taylan, Pakize; Yerlikaya-Ozkurt, Fatma (2012-01-01)
Regression analysis is a widely used statistical method for modelling relationships between variables. Multivariate adaptive regression splines (MARS) especially is very useful for high-dimensional problems and fitting nonlinear multivariate functions. A special advantage of MARS lies in its ability to estimate contributions of some basis functions so that both additive and interactive effects of the predictors are allowed to determine the response variable. The MARS method consists of two parts: forward an...
Restructuring forward step of MARS algorithm using a new knot selection procedure based on a mapping approach
Koc, Elcin Kartal; İyigün, Cem (2014-09-01)
In high dimensional data modeling, Multivariate Adaptive Regression Splines (MARS) is a popular nonparametric regression technique used to define the nonlinear relationship between a response variable and the predictors with the help of splines. MARS uses piecewise linear functions for local fit and apply an adaptive procedure to select the number and location of breaking points (called knots). The function estimation is basically generated via a two-stepwise procedure: forward selection and backward elimin...
A GENERALIZED CORRELATED RANDOM WALK APPROXIMATION TO FRACTIONAL BROWNIAN MOTION
Vardar Acar, Ceren (null; 2018-04-30)
In this study, we mainly propose an algorithm to generate correlated random walk converging to fractional Brownian motion, with Hurst parameter, H∈ [1/2,1]. The increments of this random walk are simulated from Bernoulli distribution with proportion p, whose density is constructed using the link between correlation of multivariate Gaussian random variables and correlation of their dichotomized binary variables. We prove that the normalized sum of trajectories of this proposed random walk yields a Gaussian p...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
F. Yerlikaya-Ozkurt, C. Vardar Acar, Y. Yolcu-Okur, and G.-W. Weber, “Estimation of the Hurst parameter for fractional Brownian motion using the CMARS method,”
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
, pp. 843–850, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/40852.