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

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