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

Abstract

© 2016 The Royal Statistical Society and Blackwell Publishing Ltd.The paper uses a random-weighting (RW) method to bootstrap the critical values for the Ljung-Box or Monti portmanteau tests and weighted Ljung-Box or Monti portmanteau tests in weak auto-regressive moving average 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 generalized auto-regressive conditional heteroscedasticity models. Simulation evidence indicates that the weighted portmanteau tests have a power advantage over other existing tests. A real example on the Standard and Poor's 500 index illustrates the merits of our testing procedure. As an extension, the blockwise RW method is also studied.