Fits time-varying effect models (TVEM). These are a kind of application of varying-coefficient models in the context of longitudinal data, allowing the strength of linear, logistic, or Poisson regression relationships to change over time.  These models are described further in Tan, Shiyko, Li, Li & Dierker (2012) <doi:10.1037/a0025814>.  We thank Kaylee Litson, Patricia Berglund, Yajnaseni Chakraborti, and Hanjoo Kim for their valuable help with testing the package and the documentation. The development of this package was part of a research project supported by National Institutes of Health grants P50 DA039838 from the National Institute of Drug Abuse and 1R01 CA229542-01 from the National Cancer Institute and the NIH Office of Behavioral and Social Science Research. Content is solely the responsibility of the authors and does not necessarily represent the official views of the funding institutions mentioned above. This software is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

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>.