PARAMETRIC AND NONPARAMETRIC PORTMANTEAU TESTS FOR LACK OF FIT IN TIME SERIES MODELS: A COMPARATIVE STUDY

Abstract

Several diagnostic tests for the lack of fit time series models have been introduced using parametric and nonparametric portmanteau tests. Some tests have been proposed based on the asymptotic distributions. Others are based on the Bootstrapping and Monte-Carlo significance techniques. It has been shown that the Bootstrapping and Monte-Carlo tests are robust as they provide the correct size and tend to be more powerful than those based on the asymptotic distributions. In this thesis, I conducted a comparison study of the size and power of some portmanteau tests commonly used in linear and nonlinear time series models. In particular, I considered the cases where the residuals follow Gaussian and non-Gaussian distribution under Autoregressive Moving Average (ARMA) and Generalized Autoregressive Heteroskedasticity (GARCH) models; where some parametric and nonparametric tests were applied based on the limiting distributions, Bootstrapping , and Monte-Carlo significance tests. The results show that the nonparametric Bootstrapping and Monte-Carlo significance tests provide the best performance comparing with tests based on the parametric asymptotic distribution. I applied the tests on a real application using the Qatar National Bank returns.