This article develops the asymptotic distribution of the least squares estimator of the model parameters in periodic vector autoregressive time series models (hereafter PVAR) with uncorrelated but dependent innovations. When the innovations are dependent, this asymptotic distributions can be quite different from that of PVAR models with independent and identically distributed (iid for short) innovations developed (Ursu and Duchesne in J Time Ser Anal 30:70-96, 2009). Modified versions of the Wald tests are proposed for testing linear restrictions on the parameters. These asymptotic results are illustrated by Monte Carlo experiments. An application to a bivariate real financial data is also proposed.