Autocorrelation-based tests for vector error correction models with uncorrelated but nonindependent errors

We consider in this paper the estimation and test-of-fit for vector error correction models with nonindependent innovations. The asymptotic properties of the residual sample autocorrelations are derived. It is shown that the asymptotic distribution can be quite different for models with iid innovations and models in which the innovations are nonindependent. Consequently, the usual chi-square distribution does not provide an adequate approximation of the distribution of the Box-Pierce goodness-of-fit portmanteau statistic in the presence of nonindependent innovations. We thus propose modified portmanteau and Lagrange Multiplier (LM) tests whose asymptotic distributions are a weighted sums of independent chi-squared random variables. Monte Carlo experiments illustrate the finite sample performance of the different tests.