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.

Σε αυτήν την έρευνα, κατασκευάσαμε την διορθωμένη για κίνδυνο κατάταξη αποδόσεων για την περίπτωση των ελληνικών μετοχικών αμοιβαίων κεφαλαίων. Η διορθωμένη για κίνδυνο απόδοση μετρά τη ποσότητα του κινδύνου και εκφράζεται γενικά ως αριθμός ή κατάταξη. Οι διορθωμένες για κίνδυνο αποδόσεις εφαρμόζονται σε μεμονωμένα αξιόγραφα, επενδυτικά κεφάλαια και σε χαρτοφυλάκια. Η εμμονή ορίζεται ως ένα φαινόμενο όπου η σχετική (κατάταξη) απόδοση τείνει να επαναλαμβάνεται σε διαδοχικά χρονικά διαστήματα. Εφαρμόσαμε διάφορα τεστ προκειμένου να αξιολογηθεί η παρουσία ή όχι της εμμονής. Τα εμπειρικά αποτελέσματα μας έδειξαν ότι η εμμονή γίνεται πιο αδύναμη σε μακροπρόθεσμο χρονικό ορίζοντα. / In this research we constructed the ranking of the risk adjusted returns in the case of the Greek equity mutual funds market. Risk adjusted returns is a concept that refines an investment's return by measuring how much risk is involved in producing that return, which is generally expressed as a number or rating. Risk-adjusted returns are applied to individual securities and investment funds and portfolios. Persistence is defined as a phenomenon where relative (ranked) performance tends to repeat across successive time intervals. We apply various tests in order to assess the presence or not of persistence. Our analysis documents that persistence becomes weaker as the investment horizon is increased.