This article introduces a novel class of tests for assessing time series independence based on \(\varvec{(h,\phi )} \) -divergence and quantile symbolization. We derived the asymptotic distribution of the test statistic and proposed a bootstrap alternative to enhance robustness. Simulations indicated optimal parameter values and revealed that Pearson’s divergence performs best among Rukhin and power divergence. The proposed tests demonstrated superior size-corrected power, particularly in Jensen-Shannon and Total Variation divergences across various sample sizes. Finally, the tests successfully identified dependence in stock price changes from the Tehran Stock Exchange, confirming model adequacy and the independence of residuals.
