International College of Economics and Finance

Research Seminar

May 27 at 4.40 pm, room 3402 ICEF held the Research Seminar.
Speaker: Anil K. Bera (University of Illinois at Urbana-Champaign)
May 27 at 4.40 pmroom 3402 International College of Economics and Finance held the Research Seminar.
Speaker: Anil K. Bera (University of Illinois at Urbana-Champaign)
Theme: «Scalar Measures of Volatility and Dependence for the Multivariate Models of Financial Markets»
Venue: Shabolovka str. 26, building 3, room 3402

Abstract: The variance-covariance matrix is a multi-dimensional array of numbers, gathering all the information about the individual variabilities and the pairwise linear dependence of a set of variables. However, the matrix itself is difficult to interpret in a concise way. Following Frisch(1929), we suggest a scalar measure of overall variabilities (and dependences) by collapsing all the elements in a variance-covariance matrix into a single quantity. The determinant of the covariance matrix, 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 is a measure of linear dependence. In an empirical application to the five Asian market returns, these statistics perform the intended roles successfully. In addition, these are shown to be able to reveal the empirical facts which can not be uncovered by the traditional methods. Particularly, we show that both the contagion and interdependence among the national equity markets could be confirmed in contrast to the previous studies.

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