Abstract: A method is proposed to detect lag-dependence between linear and directional time series.Jupp and Mardia （1980） proposed a correlation coellicient ρ² for bivariate angular distributionand for bivariate distributions on general manifolds. Based on their idea canonical autocorrelationfunctions and canonical partial autocorrelation functions for directional time series aredefined. These canonical antocorrelations and partial antocorrelations enable us to detect lagdependencebetween linear and directional time series as well as detecting lag-dependence between directional timeseries. This test is applied on simulated and real data with satisfactoryresults.