An improved two-step method in stochastic differential equation's structural parameter estimation

Non-parametric modelling is a method which relies heavily on data and motivated by the smoothness properties in estimating a function which involves spline and non-spline approaches. Spline approach consists of regression spline and smoothing spline. Regression spline characterised by the truncated...

Full description

Saved in:

Bibliographic Details
Main Author:	Abd. Rahman, Haliza
Format:	Thesis
Language:	English
Published:	2013
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/38022/1/HalizaAbdRahmanPFS2013.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-utm-ep.38022
record_format	uketd_dc
spelling	my-utm-ep.380222018-04-12T05:41:19Z An improved two-step method in stochastic differential equation's structural parameter estimation 2013-05 Abd. Rahman, Haliza QA Mathematics Non-parametric modelling is a method which relies heavily on data and motivated by the smoothness properties in estimating a function which involves spline and non-spline approaches. Spline approach consists of regression spline and smoothing spline. Regression spline characterised by the truncated power series basis with Bayesian approach is considered in the first step of a two-step method for estimating the structural parameters for stochastic differential equation (SDE). Previous methodology revealed the selection of knot and order of spline can be done heuristically based on a scatter plot. To overcome the subjective and tedious process of selecting the optimal knot and order of spline, an algorithm is proposed. A single optimal knot is selected out of all the points with exception of the first and the last data and the least value of Generalised Cross Validation is calculated for each order of spline. The spline model is later utilised in the second step to estimate the stochastic model parameters. In the second step, a non-parametric criterion is proposed for estimating the diffusion parameter of SDE. Linear and non-linear SDE consisting of Geometric Brownian Motion (GBM) for the former and logistic together with Lotka Volterra (LV) model for the later are tested using the two-step method for both simulated and real data. The results show high percentage of accuracy with 99.90% and 96.12% are obtained for GBM and LV model respectively for diffusion parameters of simulated data. This verifies the viability of the two-step method in the estimation of diffusion parameters of SDE with an improvement of a single knot selection. 2013-05 Thesis http://eprints.utm.my/id/eprint/38022/ http://eprints.utm.my/id/eprint/38022/1/HalizaAbdRahmanPFS2013.pdf application/pdf en public phd doctoral Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Abd. Rahman, Haliza An improved two-step method in stochastic differential equation's structural parameter estimation
description	Non-parametric modelling is a method which relies heavily on data and motivated by the smoothness properties in estimating a function which involves spline and non-spline approaches. Spline approach consists of regression spline and smoothing spline. Regression spline characterised by the truncated power series basis with Bayesian approach is considered in the first step of a two-step method for estimating the structural parameters for stochastic differential equation (SDE). Previous methodology revealed the selection of knot and order of spline can be done heuristically based on a scatter plot. To overcome the subjective and tedious process of selecting the optimal knot and order of spline, an algorithm is proposed. A single optimal knot is selected out of all the points with exception of the first and the last data and the least value of Generalised Cross Validation is calculated for each order of spline. The spline model is later utilised in the second step to estimate the stochastic model parameters. In the second step, a non-parametric criterion is proposed for estimating the diffusion parameter of SDE. Linear and non-linear SDE consisting of Geometric Brownian Motion (GBM) for the former and logistic together with Lotka Volterra (LV) model for the later are tested using the two-step method for both simulated and real data. The results show high percentage of accuracy with 99.90% and 96.12% are obtained for GBM and LV model respectively for diffusion parameters of simulated data. This verifies the viability of the two-step method in the estimation of diffusion parameters of SDE with an improvement of a single knot selection.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Abd. Rahman, Haliza
author_facet	Abd. Rahman, Haliza
author_sort	Abd. Rahman, Haliza
title	An improved two-step method in stochastic differential equation's structural parameter estimation
title_short	An improved two-step method in stochastic differential equation's structural parameter estimation
title_full	An improved two-step method in stochastic differential equation's structural parameter estimation
title_fullStr	An improved two-step method in stochastic differential equation's structural parameter estimation
title_full_unstemmed	An improved two-step method in stochastic differential equation's structural parameter estimation
title_sort	improved two-step method in stochastic differential equation's structural parameter estimation
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2013
url	http://eprints.utm.my/id/eprint/38022/1/HalizaAbdRahmanPFS2013.pdf
_version_	1747816522352427008

An improved two-step method in stochastic differential equation's structural parameter estimation

Similar Items