Analysis of the volatility in financial time series using multivariate GARCH models

Opening up of the economies and financial liberalization process at global level increased the interaction and volatility among markets. This phenomenon has made the analysis of volatility in the markets the focus of asset pricing and risk management. Analysis of the time varying volatility in the markets and the volatility spillover among markets is important for investors and portfolio managers in terms of diversification, protection and risk management. Moreover it has implications for policymakers to reveal the necessary policies by examining the reflections on macroeconomic indicators. Univariate Autoregressive Conditional Heteroscedasticity (ARCH) models have been introduced in order to model volatility and capture volatility clusters because the financial return series are autocorrelated and constant variance assumption cannot be achieved. Observing the volatility of the financial return series co-move together due to the integration in financial markets has made the transition from univariate ARCH models to Multivariate Generalized Autoregressive Conditional Heteroscedasticity (MGARCH) models necessary. The development of MGARCH models has become an important step in revealing the relationship between financial markets and financial assets. The aim of this study is to examine the co-movement of volatility between the Credit Default Swap (CDS), equity market and oil market under different statistical distributions using VAR-MGARCH models, and to determine the most appropriate model by comparing the results and to show the effect of statistical distributions on the forecast performance. Daily data of Turkey's 5year CDS premium between the dates of December 31, 2009, and February 25, 2019, BIST 30 index and Brent oil price variables are used in this study. First, VAR(1) model was applied to the conditional mean equation of the return series, and then the residuals obtained from VAR(1) model were used as an input for Diagonal BEKK-GARCH(1,1), CCC-GARCH(1,1), DCCE-GARCH(1,1) and DCCT-GARCH(1,1) models. In order to take into account the stylized features in financial return series such as fat tail and asymmetry, the models were estimated under the student-t, GED, and skewed-t distributions as well as the normal distribution. When the results of the models were analyzed and their performances were compared according to the model selection criteria, it was found that the models which handle conditional correlations dynamically had higher estimating power. When the results were examined in terms of the statistical distributions, it was seen that the skewed -t distribution was more successful than the normal, GED, and Student-t distributions. The effect of statistical distributions on forecasting performance of the models was also examined in this study. In this contex, after in-sample forecasting, Mean Square Error (MSE) and Mean Absolute Error (MAE) values were calculated for each model. When the MSE and MAE values were compared, it was concluded that the model using skewed-t in the first step and student-t distribution in the second step shows better forecasting performance. Keywords: Volatility, Multivariate GARCH Models, Credit Default Swap Premium, Oil Price, Equity Market