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) <doi:10.18637/jss.v108.i09>. 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) <doi:10.1016/j.jeconom.2013.03.006> introduces non-stationarity whereas the GARCH-X short-term component describes conditional heteroscedasticity. Maximisation by parts leads to consistent and asymptotically normal estimates.

Estimates the time-varying (tv) parameters of the GARCH(1,1) model, enabling the modeling of non-stationary volatilities by allowing the model parameters to change gradually over time. The estimation and prediction processes are facilitated through the application of the Kalman filter and state-space equations. This package supports the estimation of tv parameters for various deterministic functions, which can be identified through exploratory analysis of different time periods or segments of return data. The methodology is grounded in the framework presented by Ferreira et al. (2017) <doi:10.1080/00949655.2017.1334778>.

Probability mass (d), distribution (p), quantile (q), and random 
    number generating (r and rt) functions for the time-varying right-truncated 
    geometric (tvgeom) distribution. Also provided are functions to calculate the first 
    and second central moments of the distribution. The tvgeom distribution
    is similar to the geometric distribution, but the probability 
    of success is allowed to vary at each time step, and there are a limited 
    number of trials. This distribution is essentially a Markov chain, and it
    is useful for modeling Markov chain systems with a set 
    number of time steps.