Bootstrapping the portmanteau tests in weak auto-regressive moving average models

This paper uses a random weighting (RW) method to bootstrap the critical values for the Ljung-Box/Monti portmanteau tests and weighted Ljung-Box/Monti portmanteau tests in weak ARMA models. Unlike the existing methods, no user-chosen parameter is needed to implement the RW method. As an application, these four tests are used to check the model adequacy in power GARCH models. Simulation evidence indicates that the weighted portmanteau tests have the power advantage over other existing tests. A real example on S&P 500 index illustrates the merits of our testing procedure. As one extension work, the block-wise RW method is also studied.