A new statistic to the theory of correlation stability testing in financial market

Testing the stability of correlation structures is an active research area involving the applications of multivariate analysis in financial market such as stock market analysis, risk management, market equity, general financial and economic studies, and real estates. In the financial market, the num...

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Main Author:	Sharif, Shamshuritawati
Format:	Thesis
Language:	English
Published:	2013
Subjects:	HF Commerce QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/33758/5/ShamshuritawatiSharifPFS2013.pdf
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spelling	my-utm-ep.337582017-07-23T01:30:35Z A new statistic to the theory of correlation stability testing in financial market 2013-04 Sharif, Shamshuritawati HF Commerce QA Mathematics Testing the stability of correlation structures is an active research area involving the applications of multivariate analysis in financial market such as stock market analysis, risk management, market equity, general financial and economic studies, and real estates. In the financial market, the number of variable p is usually large and might reach thousands. As a consequence, the standard stability test Box’s M and Jennrich’s statistic are not capable to handle it. This condition makes the computation of the statistical tests quite cumbersome and tedious because the computational efficiency of finding the determinant and inverse of the correlation matrix becomes low. In order to solve these problems, this thesis introduces T-statistic for testing the stability of correlation structure in an independent sequence of sample correlation matrices from a p-variate normal distribution based on a repeated test approach. For this purpose, the asymptotic distribution of the test under the null hypothesis is derived mathematically using the vec operator and commutation matrix. The power of T-statistic is computed and compared with existing ones under certain conditions of the alternative hypothesis. It is found that, if p is large, then the power of T*-statistic dominates the power of the J-statistic for all shifts. On the other hand, when the shift is small, its power is equal to that the Mstatistic. The second problem is to diagnose and find an explanation when the null hypothesis is rejected. For that purpose, by considering correlation matrix as representing a complex network, network topology approach is used to demonstrate to what extent that two or more correlation structures are different from each other. To interpret the filtered network topology, four popular centrality measures have been used. Moreover, to enrich the economic interpretation, average of weights is introduced as another measure of centrality. 2013-04 Thesis http://eprints.utm.my/id/eprint/33758/ http://eprints.utm.my/id/eprint/33758/5/ShamshuritawatiSharifPFS2013.pdf application/pdf en public http://dms.library.utm.my:8080/vital/access/manager/Repository/vital:69893?site_name=Restricted Repository phd doctoral Universiti Teknologi Malaysia, Faculty of Science Faculty of Science
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	HF Commerce QA Mathematics
spellingShingle	HF Commerce QA Mathematics Sharif, Shamshuritawati A new statistic to the theory of correlation stability testing in financial market
description	Testing the stability of correlation structures is an active research area involving the applications of multivariate analysis in financial market such as stock market analysis, risk management, market equity, general financial and economic studies, and real estates. In the financial market, the number of variable p is usually large and might reach thousands. As a consequence, the standard stability test Box’s M and Jennrich’s statistic are not capable to handle it. This condition makes the computation of the statistical tests quite cumbersome and tedious because the computational efficiency of finding the determinant and inverse of the correlation matrix becomes low. In order to solve these problems, this thesis introduces T-statistic for testing the stability of correlation structure in an independent sequence of sample correlation matrices from a p-variate normal distribution based on a repeated test approach. For this purpose, the asymptotic distribution of the test under the null hypothesis is derived mathematically using the vec operator and commutation matrix. The power of T-statistic is computed and compared with existing ones under certain conditions of the alternative hypothesis. It is found that, if p is large, then the power of T*-statistic dominates the power of the J-statistic for all shifts. On the other hand, when the shift is small, its power is equal to that the Mstatistic. The second problem is to diagnose and find an explanation when the null hypothesis is rejected. For that purpose, by considering correlation matrix as representing a complex network, network topology approach is used to demonstrate to what extent that two or more correlation structures are different from each other. To interpret the filtered network topology, four popular centrality measures have been used. Moreover, to enrich the economic interpretation, average of weights is introduced as another measure of centrality.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Sharif, Shamshuritawati
author_facet	Sharif, Shamshuritawati
author_sort	Sharif, Shamshuritawati
title	A new statistic to the theory of correlation stability testing in financial market
title_short	A new statistic to the theory of correlation stability testing in financial market
title_full	A new statistic to the theory of correlation stability testing in financial market
title_fullStr	A new statistic to the theory of correlation stability testing in financial market
title_full_unstemmed	A new statistic to the theory of correlation stability testing in financial market
title_sort	new statistic to the theory of correlation stability testing in financial market
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2013
url	http://eprints.utm.my/id/eprint/33758/5/ShamshuritawatiSharifPFS2013.pdf
_version_	1747816177921425408

A new statistic to the theory of correlation stability testing in financial market

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