On the finite-sample distribution of modified portmanteau tests for randomness of a Gaussian time series

This paper proposes three modified portmanteau tests based on the applications of the Fisher (1921) and Hotelling (1953) transformations to sample autocorrelations. The test statistics are asymptotically chi-square. Our simulation results indicate that the empirical significance levels of the proposed tests are more reliable than the portmanteau tests of Box & Pierce (1970), Ljung & Box (1978) and Dufour & Roy (1986) when the sample size is small (15 less than or equal to n less than or equal to 40) and the number of sample autocorrelations is large (m greater than or equal to 7).