Abd.Rahman, Haliza and Bahar, Arifah and Rosli, Norhayati and Md. Salleh, Madihah
(2010)
*Parameter estimation of stochastic differential equation : Bayesian regression.*
Jurnal KALAM, 3
(1).
ISSN 1985 – 5222

Full text not available from this repository.

Official URL: https://jurnalkalam.wordpress.com/volume-3-%E2%99%...

## Abstract

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.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Bayesian approach, regression spline, stochastic differential equation |

Subjects: | Q Science > QA Mathematics |

Divisions: | Science |

ID Code: | 25965 |

Deposited By: | Narimah Nawil |

Deposited On: | 22 Jun 2012 03:39 |

Last Modified: | 30 Nov 2018 06:22 |

Repository Staff Only: item control page