Time series model validity tests based on general correlations are presented in this paper. It is shown that the tests Φxixi(τ), Φxixi2(τ) and Φxixixi(τ1, t2) can only detect a subset of any possible unmodelled terms in the residuals, whereas Φxi2xi2(τ) detects all possible terms. These basic results are then extended to include functions of process or residual terms as entries in the correlation. Simulation studies are included to demonstrate the effectiveness of the tests when applied to estimated models of both simulated and real data sequences.