Abstract: This paper develops a general nonparametric test for the null hypothesis that the vector of time series under scrutiny is temporally and cross sectionally independent. This test can be used to test the adequacy of a fitted model. We can diagnostically test a vector autoregressive model fitted to given data. This procedure is legitimate because the first order asymptotic distribution of the test statistic is robust with respect to the estimated residual vector.
Key words and phrases: Chaos, BDS test, Denker-Keller projection, U-statistic, V-statistic, vector autoregressive model.