Testing serial independence using maximum Phi-entropy with quantile symbolization

This research introduces a novel class of tests for assessing time series independence, utilizing Phi-entropy and a framework based on quantile symbolization. We derived the asymptotic distribution of the test statistic and developed a bootstrap version to ensure robust performance, which was subsequently validated for consistency. Simulations identified the optimal parameter values for the test, and comparisons with existing methods demonstrated its superior performance, particularly when using the Gini-Simpson index, which achieved the highest size-corrected power. Finally, applying the test to data from the Tehran Stock Exchange effectively detected dependencies, validated model fit, and confirmed the independence of residuals.