Neural Generalised AutoRegressive Conditional Heteroskedasticity

In the univariate setting, popular methods include Autoregressive Conditional Heteroskedastic models (ARCH) (Engle 1982) and Generalised GARCH (GARCH) models (Bollerslev 1986). ARCH and GARCH models are regression-based models estimated using maximum likelihood, and are capable of capturing stylised facts about financial time series such as volatility clustering (Bauwens et al. 2006). The ARCH(p) model describes the conditional volatility as a function of p lagged squared residuals, and similarly the GARCH(p,q) model include contributions due to the last q conditional variances. Many variants of the GARCH model have been proposed to better capture properties of financial time series, for example the EGARCH (Nelson 1991) and GJR-GARCH (Glosten et al. 1993) models were designed to capture the so-called leverage effect, which describes the negative relationship between asset price and volatility. In a multivariate setting, instead of modelling only time-varying conditional variances, for an n-dimensional system, we estimate the n n time-varying variance-covariance matrix. This allows us to investigate interactions between the volatility of different time series and whether there is a transmission of volatility (spillover effect) between markets (Bauwens et al. 2006, Erten et al. 2012). Popular multivariate GARCH models include the VEC model (Bollerslev et al. 1988), the