A new semiparametric observation-driven volatility model is proposed. In contrast to the standard semiparametric generalized autoregressive conditional heteroskedasticity (GARCH) model, the form of the error density has a direct influence on both the semiparametric likelihood and the volatility dynamics. The estimator is shown to consistently estimate the conditional pseudo true parameters of the model. Simulation-based evidence and an empirical application to stock return data confirm that the new statistical model realizes substantial improvements compared to GARCH type models and quasi-maximum likelihood estimation if errors are fat-tailed and possibly skewed.
Blasques, F., Ji, J., & Lucas, A. (2016). Semiparametric score driven volatility models. Computational Statistics and Data Analysis, 100, 58–69. https://doi.org/10.1016/j.csda.2015.04.003