Application and comparison of GARCH and GJR models for volatility modelling

Modelling of financial time series is related to two issues, which are necessary to deal with: fat tails of probability distributions and volatility clustering. Both issues were already tackled with different approaches. At present the distributions such as Student, normal-inverse Gaussian, variance-gamma and others are applied to model the time series of returns. On the other hand, the conditionality of variance is usually modelled by some type of model similar to the GARCH model. In this paper we assume GARCH model and its modification GIR model with both Gaussian and Student distributions for FX returns modelling. The goal of the paper is to apply these models on chosen FX time series and check the statistical significance of particular parameters as well as the assumption about the probability distribution of residuals.