Time Varying GARCH Modelling

Simulation, estimation and inference for univariate and multivariate TV(s)-GARCH(p,q,r)-X models, where s indicates the number and shape of the transition functions, p is the ARCH order, q is the GARCH order, r is the asymmetry order, and 'X' indicates that covariates can be included; see Campos-Martins and Sucarrat (2024) . In the multivariate case, variances are estimated equation by equation and dynamic conditional correlations are allowed. The TV long-term component of the variance as in the multiplicative TV-GARCH model of Amado and Terasvirta (2013) introduces non-stationarity whereas the GARCH-X short-term component describes conditional heteroscedasticity. Maximisation by parts leads to consistent and asymptotically normal estimates.