Bootstrapping the Li-Mak and McLeod-Li Portmanteau Tests for GARCH Models

In this paper, blocks-of-blocks (BOB) bootstrap method is employed for the commonly used diagnostic tests for generalized autoregressive conditional heteroscedastic (GARCH) models. More specifically, the single block-of-blocks and double blocks-of-blocks bootstrap techniques, using three different block lengths of size 4, 10, and 20, are implemented for bootstrapping the Li-Mak and Mcleod-Li portmanteau tests. Using Monte Carlo simulations, the size and power of both tests under the standard normal and Student-t errors are investigated. It was found that the discrepancy between the true and nominal probability of rejection was reduced for both the tests using single block-of-blocks and double blocks-of-blocks bootstrap methods. The power of the Li-Mak test for the GARCH (1, 1) model was found slightly better than the Mcleod-Li test. An empirical example using the monthly data of currency exchange rate (US $ per Pak Rupees) is also reported.