| Financial Market asset do not follow a Gaussian distribution path, but exhibit unconditional density characteristics in which dynamic linear models fail to capture. Hence non-linear estimation models have been developed to capture the variance in returns, and plenty of research has been dedicated to this area starting from the early GARCH model developed by Engle (1982). But we are more interested in looking at models that adequately estimate and interpret correlation dynamics over a 5-year period of a five-dimensional dataset. The stochastic models we have investigated in this study are the Diagnonal BEKK, Constant Conditional Correlation (CCC-GARCH), and Diagonal Conditional Correlation (DCC-GARCH) models. We estimate these models using an econometrics package combined with program coding that provide the correlation dynamics we are looking for. Positive correlation of conditional time-varying correlations were detected amongst the Diagonal BEKK and the DCC-MGARCH, and suggested rankings criteria propose findings that are dependent on what preferences the portfolio or risk manager takes in model selection in pricing assets and hedging strategies, although this study leans towards the diagonal BEKK from the results obtained due to the ease of parametric estimation. We conclude the CCC-MGARCH although widely popular, is too restrictive in many empirical appliciations due to the assumption of being time-invariant to ensure covariance matrix positive definiteness, and is therefore not a likely candidate in time-varying correlation estimation. |
