Journal of Statistics Applications & Probability

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This paper presents two new portmanteau tests to evaluate the goodness of fit of ARMA models. The tests are based on exponential weights of the residual autocorrelation function and the residual partial autocorrelation function. A review of previous work on portmanteau tests is given. The performance of the new portmanteau tests is compared with previous portmanteau tests via the use of Monte Carlo experiments with 10,000 replications. The empirical size simulations show that, when an AR(1) process is fitted by an AR(1) model, most portmanteau tests from previous studies do not have significance levels that are stable with respect to lag length. The new residual partial autocorrelation function test is shown to outperform previous tests in terms of its power and its stability with respect to lag length.

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