We describe a test, based on the correlation integral, for the independence of a variable and a vector that can be used with serially dependent data. Monte Carlo simulations suggest that the test has good power to detect dependence in several models, performing nearly as well or better than the BDS test in univariate time series and complementing the BDS test in distributed lag models. Finally, we apply our test in conjunction with the BDS test to examine models of US unemployment rates.