Utilizing symmetric Phi-divergence in serial independence testing

This manuscript introduces a novel class of time series independence tests based on Phi-divergence and quantile-based symbolization. We derive the asymptotic distribution of the test statistic and propose a bootstrap version. Simulations identified optimal parameter values and compared the test performance to existing methods, demonstrating higher size-corrected power for specific Phi-divergence cases. Furthermore, we investigate Rukhin and power divergence, revealing Pearson’s divergence as optimal. The proposed tests were applied to financial (Tehran Stock Exchange, S\&P 500) and ecological (Lynx population) datasets, effectively detecting dependence on the data and confirming the adequacy of the model through independent residuals, demonstrating the robustness and versatility of the method in diverse domains.