An entropy divergence, D-distribution and its selected application in multivariate financial time series
by G.S. David Sam Jayakumar; A. Sulthan; W. Samuel
International Journal of Financial Services Management (IJFSM), Vol. 11, No. 2, 2021

Abstract: This paper proposes an Entropy Divergence (ED) which is the difference between the two Shannon's differential entropies for multivariate discrete and continuous distributions. This is illustrated based on the multivariate version of the central limit theorem to evaluate the divergence between the multivariate scaled normal distribution (f) and scaled student's t distribution (g). This helps to firmly establish the exact distribution of ED, and its density is visualised in terms of Meijer G function. Moreover, the authors derived the distribution of the difference (D) between two EDs in terms of the sum of p-variate independent Fisher's-Z variable plus a normalising constant. Similarly, the moments of the two cases are derived which are visualised through digamma and poly-gamma functions. The percentage points of ED distribution of p-variates are computed at 5% and 1% significance level for respective degrees of freedom. Plots show the percentage points (discrepancy distance) between the multivariate distribution (normal) of financial time series and the distribution of cross-section data (student's t) graphically. The proposed ED is applied to test the sphericity of Nifty 50 stock returns in National Stock Exchange. Similarly, D-statistic is used to check the equality of two Shannon's differential entropy, where returns are grouped based on the demonetisation crisis as before and after in India.

Online publication date: Mon, 17-Jan-2022

The full text of this article is only available to individual subscribers or to users at subscribing institutions.

 
Existing subscribers:
Go to Inderscience Online Journals to access the Full Text of this article.

Pay per view:
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.

Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Financial Services Management (IJFSM):
Login with your Inderscience username and password:

Username:        Password:          Forgotten your password?

Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.

If you still need assistance, please email subs@inderscience.com