This paper presents a new category of tests for assessing time series independence using \((h, \phi )\) -divergence and quantile-based symbolization. We derived the test statistic’s asymptotic distribution and proposed a bootstrap version to enhance reliability. Simulation analyses identified optimal parameter values and showed that the proposed tests outperform existing methods in size-corrected power, particularly in Jensen-Shannon, Pearson, Cubic, and Total Variation divergences for various sample sizes. Finally, we applied these tests to stock price data from the Tehran Stock Exchange, confirming the presence of dependence and validating model adequacy.
