Evaluating first passage times in Markov chains from the perspective of asymptotic and empirical information

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Gül M., Çelebioğlu S.

Ordu Üniversitesi Bilim ve Teknoloji Dergisi, vol.3, no.1, pp.27-45, 2013 (Peer-Reviewed Journal)

• Publication Type: Article / Article
• Volume: 3 Issue: 1
• Publication Date: 2013
• Journal Name: Ordu Üniversitesi Bilim ve Teknoloji Dergisi
• Page Numbers: pp.27-45
• Eskisehir Osmangazi University Affiliated: No

Abstract

First passage times underlie many stochastic processes in which the event, such as a chemical reaction,

the firing of a neuron, or the triggering of a stock option, relies on a variable reaching a specified value

for the first time. In this study, a transition matrix was estimated by taking into account the closing

values of Istanbul Stock Exchange (ISE -100) index from 20.01.2009 to 18.01.2013 for discrete

Markov model. Empirical information regarding the first passage time was obtained by writing a

computer program. Later, the first passage time which calculated by using WinQSB software was

accepted as asymptotic information. Under the assumption that the frequency distribution of the first

passage time fits with the geometric distribution, the fittings of the first passage time obtained from

empirical information and the first passage time obtained from asymptotic information to the

geometric distribution was compared with a chi-square analysis. It is found that, in some cases of the

first passage time of asymptotic information gives better results regarding the fitting with the

geometric distribution. Graphics of continuous distribution which comply with frequency of first

passage time were also provided by using Easy-fit software. From these graphs first passage time

distribution was seen to be a positively skewed or reverse j-shaped distribution.