In this paper we investigate the size and power properties of some common tests for autocorrelation when applied to high-dimensional data. This includes cases when the dimension of data increases with the sample size. A total of seven tests, of which one is proposed by the authors, are investigated through Monte Carlo simulations. We include several functional forms of the autoregressive parameter and the residual covariance matrix to assess the tests. It is shown that all included standard tests fail either in terms of size or power if the dimension of data is close to the sample size, while the new test has good overall properties.