The dependence of Polish stock subindexes on the DJIA: the use of Rubin causality

In this paper, the Rubin’s causality framework is employed to examine changes in causality between the returns of DJIA and the returns of Polish sectoral indexes over a six-year period (2018–2023), which includes both the COVID-19 pandemic and, since February 24, 2022, the Russo-Ukrainian war. Causality was tested across the entire period as well as within two-years subperiods. The primary objective was to assess the stability and significance of causality during these intervals. The tests were conducted for the continuous returns, which were clustered into two groups labelled 0 and 1 within these temporally restricted samples. Group 0 consists of days following a decline in the previous day’s DJIA closing price. Group 1 includes days following an increase in the previous day’s DJIA quotation. The main goal was to determine whether there exists a statistically significant difference between the distribution of logarithmic returns in the two groups. We applied several tests, including the Kolmogorov–Smirnov, Wilcoxon, the multivariate Wilcoxon test with Tukey and projection depth, and the Brown–Forsythe tests. Among the analyzed subindexes, three distinct groups were identified. The detailed results of the computations and tests are presented in the tables. Finally, the authors suggest directions for future research.