Scalar Measures of Volatility and Dependence for the Multivariate Models with Applications to Asian Financial Markets

Sangwhan Kim and Anil K. Bera ()
Additional contact information
Sangwhan Kim: Department of Economics, Chungbuk National University, Chungbuk 28644, Republic of Korea
Anil K. Bera: Department of Economics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

JRFM, 2023, vol. 16, issue 4, 1-16

Abstract: The variance–covariance matrix is a multi-dimensional array of numbers, containing information about the individual variabilities and the pairwise linear dependence of a set of variables. However, the matrix itself is difficult to represent in a concise way, particularly in the context of multivariate autoregressive conditional heteroskedastic models. The common practice is to report the plots of k ( k − 1 ) / 2 time-varying pairwise conditional covariances, where k is the number of markets (or assets) considered; thus, when k = 10 , there will be 45 graphs. We suggest a scalar measure of overall variabilities (and dependences) by summarizing all the elements in a variance–covariance matrix into a single quantity. The determinant of the covariance matrix Σ , called the generalized variance , can be used as a measure of overall spread of the multivariate distribution. Similarly, the positive square root of the determinant | R | of the correlation matrix, called the scatter coefficient , will be a measure of linear independence among the random variables, while collective correlation + ( 1 − | R | ) 1 / 2 will be an overall measure of linear dependence. In an empirical application to the six Asian market returns, these statistics perform the intended roles successfully. In addition, these are shown to be able to reveal and explain the empirical facts that cannot be uncovered by the traditional methods. In particular, we show that both the contagion and interdependence (among the national equity markets) are present and could be quantitatively measured in contrast to previous studies, which revealed only market interdependence.

Keywords: generalized variance; collective correlation; scatter coefficient; multivariate GARCH models (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/1911-8074/16/4/212/pdf (application/pdf)
https://www.mdpi.com/1911-8074/16/4/212/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jjrfmx:v:16:y:2023:i:4:p:212-:d:1108433

Access Statistics for this article

JRFM is currently edited by Ms. Chelthy Cheng

More articles in JRFM from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().