This study presents a novel framework for testing independence in time series using \((h,\phi )\) -divergence and quantile symbolization. We derived the asymptotic distribution of the test statistic and proposed a bootstrap method to enhance reliability. The simulation results showed that "Cressie and Read" and "Rukhin" divergences are optimal when aligned with Pearson’s divergence, while Rényi is optimal for cubic divergence. The proposed tests demonstrated superior size-corrected power compared to existing methods, particularly in Jensen-Shannon and Total Variation divergences across various sample sizes. Finally, applications to stock price data from the Tehran Stock Exchange confirmed the method’s effectiveness in detecting dependence and validating model adequacy.
