Two Tests for Dependence (of Unknown Form) between Time Series

This paper proposes two new nonparametric tests for independence between time series. Both tests are based on symbolic analysis, specifically on symbolic correlation integral, in order to be robust to potential unknown nonlinearities. The first test is developed for a scenario in which each considered time series is independent and therefore the interest is to ascertain if two internally independent time series share a relationship of an unknown form. This is especially relevant as the test is nuisance parameter free, as proved in the paper. The second proposed statistic tests for independence among variables, allowing these time series to exhibit within-dependence. Monte Carlo experiments are conducted to show the empirical properties of the tests.This research is the result of the activity performed under the program Groups of Excellence of the Region of Murcia, the Fundación Seneca, Science and Technology Agency of the region of Murcia project under grant 19884/GERM/15. All remaining errors are our responsibility