Macroeconomic and financial applications of S-vine copula models for time series

This thesis investigates the modelling and prediction of macroeconomic and financial time series by using S-vine models and vt-S-vine models. The first contribution of this thesis is to demonstrate that non-linear and non-Gaussian models in the class of S-vine processes can fit better than autoregressive moving average (ARMA) models for certain types of macroeconomic time series, such as inflation rates. The S-vine processes generalize the class of Gaussian ARMA models by modelling dependencies using pair copulas and by modelling marginal behaviour using arbitrary continuous distributions. The second part of this thesis concerns the modelling and forecasting the volatile financial returns series by vt-S-vine models. Returns are traditionally estimated by using the generalized autoregressive conditionally heteroscedastic (GARCH) type processes or variants. We show that the vt-S-vine models can compete with GARCH processes in many cases. In order to reveal the statistical properties and structures of GARCH type processes, the vt-S-vine models are applied to replicate GARCH type processes. The best combinations of margins and pair copulas in vt-S-vines for replicating GARCH type processes are determined. The higher-order vt-S-vine processes with a sequence of mixed pair copulas can mimic GARCH type processes more precisely than first-order or second-order S-vine with t copulas as proposed by previous studies. The final part of this thesis is devoted to the application of vt-S-vines in the trading book of banks. The value-at-risk (VaR) and the VaR exceedance probabilities are estimated in vt-S-vine processes, where the best quantile estimation methods are presented in each case. Surprisingly, the quantile estimator that is closest on average to the true value of the quantile of a distribution may not be the one that yields the most accurate value for the exceedance probability. Vt-S-vines are very flexible and promising models for stationary macroeconomic, financial and banking time series, and deserve to be widely used and rapidly developed in future.