For an ARMA adequacy test, Box and Pierce (1970) proposed a portmanteau test TBP. However, because the accuracy of TBP by x^2-approximation is not good, various modifications of TBP have been introduced by many authors. Taniguchi and Amano (2008) proposed an important portmanteau test TWLR of natural Whittle type which is always asymptotically x^2 distributed under the null hypothesis that ARMA model is adequate. This paper compares TWLR with another famous portmanteau tests Ljung-Box's TLB, Li-McLeod's TLM and Monti's TMN and proves its accuracy by simulation. Empirical powers of those portmanteau tests are also compared numerically.