Diagnostic Checking For Linearity in Time Series Models

Abstract

In this thesis, I studied the well-known portmanteau tests appearing in the time series literature. In particular, I interest in reviewing the test statistics that can be used to check the adequacy of the fitted Autoregressive and Moving Average (ARMA) models, the Generalized Conditional Heteroskedasticity (GARCH) models, and special nonlinear models that are proposed early and widely used specially in financial time series. I estimate the empirical levels of these tests based on the Monte Carlo significance tests and show that the Monte-Carlo tests provide an accurate estimate for these levels. I conduct a simulation power comparison between these tests and show that the Monte-Carlo significance test presented based on the determinant of a matrix which include four matrices of auto correlation of residual, auto correlation of squared residual and cross correlation between the residual and squared residuals has higher power than the other tests in many cases. I demonstrate the usefulness of the Monte-Carlo tests by applying these tests on the daily log-returns of Ooredoo Qatar.