Parameter estimation of stochastic differential equation

Non-parametric modeling 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 with Bayesian approach is consid...

Full description

Bibliographic Details
Main Authors:	Haliza Abd. Rahman, Arifah Bahar, Norhayati Rosli, Madihah Md. Salleh
Format:	Article
Language:	English
Published:	Universiti Kebangsaan Malaysia 2012
Online Access:	http://journalarticle.ukm.my/5683/ http://journalarticle.ukm.my/5683/ http://journalarticle.ukm.my/5683/1/19%2520Haliza%2520Abd%2520Rahman.pdf

id	ukm-5683
recordtype	eprints
spelling	ukm-56832016-12-14T06:39:11Z http://journalarticle.ukm.my/5683/ Parameter estimation of stochastic differential equation Haliza Abd. Rahman, Arifah Bahar, Norhayati Rosli, Madihah Md. Salleh, Non-parametric modeling 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 with Bayesian approach is considered in the first step of a two-step method in estimating the structural parameters for stochastic differential equation (SDE). The selection of knot and order of spline can be done heuristically based on the scatter plot. To overcome the subjective and tedious process of selecting the optimal knot and order of spline, an algorithm was proposed. A single optimal knot is selected out of all the points with exception of the first and the last data which gives the least value of Generalized Cross Validation (GCV) for each order of spline. The use is illustrated using observed data of opening share prices of Petronas Gas Bhd. The results showed that the Mean Square Errors (MSE) for stochastic model with parameters estimated using optimal knot for 1,000, 5,000 and 10,000 runs of Brownian motions are smaller than the SDE models with estimated parameters using knot selected heuristically. This verified the viability of the two-step method in the estimation of the drift and diffusion parameters of SDE with an improvement of a single knot selection. Universiti Kebangsaan Malaysia 2012-12 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/5683/1/19%2520Haliza%2520Abd%2520Rahman.pdf Haliza Abd. Rahman, and Arifah Bahar, and Norhayati Rosli, and Madihah Md. Salleh, (2012) Parameter estimation of stochastic differential equation. Sains Malaysiana, 41 (12). pp. 1635-1642. ISSN 0126-6039 http://www.ukm.my/jsm/
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
language	English
description	Non-parametric modeling 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 with Bayesian approach is considered in the first step of a two-step method in estimating the structural parameters for stochastic differential equation (SDE). The selection of knot and order of spline can be done heuristically based on the scatter plot. To overcome the subjective and tedious process of selecting the optimal knot and order of spline, an algorithm was proposed. A single optimal knot is selected out of all the points with exception of the first and the last data which gives the least value of Generalized Cross Validation (GCV) for each order of spline. The use is illustrated using observed data of opening share prices of Petronas Gas Bhd. The results showed that the Mean Square Errors (MSE) for stochastic model with parameters estimated using optimal knot for 1,000, 5,000 and 10,000 runs of Brownian motions are smaller than the SDE models with estimated parameters using knot selected heuristically. This verified the viability of the two-step method in the estimation of the drift and diffusion parameters of SDE with an improvement of a single knot selection.
format	Article
author	Haliza Abd. Rahman, Arifah Bahar, Norhayati Rosli, Madihah Md. Salleh,
spellingShingle	Haliza Abd. Rahman, Arifah Bahar, Norhayati Rosli, Madihah Md. Salleh, Parameter estimation of stochastic differential equation
author_facet	Haliza Abd. Rahman, Arifah Bahar, Norhayati Rosli, Madihah Md. Salleh,
author_sort	Haliza Abd. Rahman,
title	Parameter estimation of stochastic differential equation
title_short	Parameter estimation of stochastic differential equation
title_full	Parameter estimation of stochastic differential equation
title_fullStr	Parameter estimation of stochastic differential equation
title_full_unstemmed	Parameter estimation of stochastic differential equation
title_sort	parameter estimation of stochastic differential equation
publisher	Universiti Kebangsaan Malaysia
publishDate	2012
url	http://journalarticle.ukm.my/5683/ http://journalarticle.ukm.my/5683/ http://journalarticle.ukm.my/5683/1/19%2520Haliza%2520Abd%2520Rahman.pdf
first_indexed	2023-09-18T19:44:50Z
last_indexed	2023-09-18T19:44:50Z
_version_	1777405830699679744

Parameter estimation of stochastic differential equation

Similar Items