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

On the distribution of the sample autocorrelation coefficients

“…The dashed lines represent the actual probabilities of rejection for Q DR . The figures show that there is still an over-rejection problem with Q DR , and this over-rejection problem is also documented by Dufour and Roy (1986) and Kwan and Sim (1996). The dotted lines represent the actual probabilities of rejection for Q KS .…”

“…Despite the simplicity of the adjusted Box-Pierce test, its size is almost correct and compares quite favorably with the other modified portmanteau tests. Therefore, we believe the adjusted Box-Pierce test statistic is a better choice than the modified portmanteau tests by Dufour and Roy (1986) and Kwan and Sim (1996).…”

“…One of the earlier attempts is by Dufour and Roy (1986). They suggest the test statistic Another attempt is by Kwan and Sim (1996) who propose the following test statistic…”

“…11 Instead of using second and fourth equations in Box I, Kwan and Sim (1996) use approximate formulas from Davies et al (1977) …”

“…Note that Dufour and Roy (1986) and Kwan and Sim (1996) also propose other more complicated versions of their modified portmanteau tests. We have also analyzed the other modified portmanteau tests and they perform similarly to the tests reported in here.…”