Multivariate Statistical Analysis in the Study of Capital Markets - Budny, Katarzyna; Tatar, Jan (Krakow Review of Economics and Management/Zeszyty Naukowe Uniwersytetu Ekonomicznego w Krakowie, 2018)
In their previous work, the authors have presented an approach to describing and researching multivariate probability distributions that departs from the standard. In this paper, the new tools that resulted have been used to research and analyse selected two-, three- and fourth-dimension random vectors that have appeared on the Polish capital market. Coordinates of these vectors are stock market indices: WIG, WIG-20, WIG-Banks, WIG-Fuels and profitability of these indices. Using market data for the period 4/1/16–7/7/17, the following estimators of parameters of analysed distributions were calculated and interpreted: expected value, total variance, total standard deviation, skewness coefficient, norm of the skewness coefficient, square of the skewness coefficient, kurtosis and excess coefficient. In order to overview and compare, for each vector a covariance matrix and a matrix of correlation coefficients are indicated. The following characteristics of marginal distributions are also used: expected value, variance, standard deviation, skewness coefficient, kurtosis and excess coefficient. For each pair of financial random vectors researched, the estimator of the square of correlation coefficient was also calculated, as that is one of the possible measures of their dependence.