Higher order generalisation of first order autoregressive tests

Higher order analogues of currently favoured tests for autocorrelated dicturbances are presented. Comparisons of power, against autoregressive disturbances of a range of orders considered likely in practice, favour a version of a test originally proposed by King (1985). This superiority is particularly marked with regressors for which Ordinary Least Squares is least efficient and thus testing most crucial. Selected significance bounds are tabulated for the twelfth order analogue of this test statistic for use with monthly data.