This thesis analyses, derives and evaluates specification tests of Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH) regression models, both univariate and multivariate. Of particular interest, in the first half of the thesis, is the derivation of robust test procedures designed to assess the Constant Conditional Correlation (CCC) assumption often employed in multivariate GARCH (MGARCH) models. New asymptotically valid conditional moment tests are proposed which are simple to construct, easily implementable following the full or partial Quasi Maximum Likelihood (QML) estimation and which are robust to non-normality. In doing so, a non-normality robust version of the Tse's (2000) LM test is provided. In addition, a new and easily programmable expressions of the expected Hessian matrix associated with the QMLE is obtained. The finite sample performances of these tests are investigated in an extensive Monte Carlo study, programmed in GAUSS.In the second half of the thesis, attention is devoted to nonparametric testing of GARCH regression models. First simultaneous consistent nonparametric tests of the conditional mean and conditional variance structure of univariate GARCH models are considered. The approach is developed from the Integrated Generalized Spectral (IGS) and Projected Integrated Conditional Moment (PICM) procedures proposed recently by Escanciano (2008 and 2009, respectively) for time series models. Extending Escanciano (2008), a new and simple wild bootstrap procedure is proposed to implement these tests. A Monte Carlo study compares the performance of these nonparametric tests and four parametric tests of nonlinearity and/or asymmetry under a wide range of alternatives. Although the proposed bootstrap scheme does not strictly satisfy the asymptotic requirements, the simulation results demonstrate its ability to control the size extremely well and therefore the power comparison seems justified. Furthermore, this suggests there may exist weaker conditions under which the tests are implementable. The simulation exercise also presents the new evidence of the effect of conditional mean misspecification on various parametric tests of conditional variance. The testing procedures are also illustrated with the help of the S&P 500 data. Finally the PICM and IGS approaches are extended to the MGARCH case. The procedure is illustrated with the help of a bivariate CCC-GARCH model, but can be generalized to other MGARCH specifications. Simulation exercise shows that these tests have satisfactory size and are robust to non-normality. The marginal mean and variance tests have excellent power; however the covariance marginal tests lack power for some alternatives.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:553365 |
| Date | January 2011 |
| Creators | Shadat, Wasel Bin |
| Contributors | Orme, Chris; Gill, Leonard; Hall, Alastair |
| Publisher | University of Manchester |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://www.research.manchester.ac.uk/portal/en/theses/specification-testing-of-garch-regression-models(56c218db-9b91-4d8c-bf26-8377ab185c71).html |
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