QMSLV: a gretl package for quasi maximum likelihood estimation of stochastic volatility models

The paper presents a gretl package, QMLSV, for quasi-maximum likelihood (QML) estimation of univariate stochastic volatility (SV) models. Unlike univariate GARCH models, which include only a single random component (return innovation) affecting return but not volatility, SV models also include a volatility innovation, which affect volatility and makes model estimation a challenging task. QML estimation is one of the most well-established methods to address that task. In addition to the standard QLM method (Ruiz, 1994; Harvey, Ruiz, Shephard, 1994) based on the assumption that volatility and return innovations are not correlated (symmetric volatility), QMLSV also includes two methods for asymmetric volatility models, i.e. models in which volatility innovation is correlated with return innovation. The first of these is the modified QML method proposed by Harvey and Shephard in 1996, which provides a volatility predictor mainly similar to the Threshold GARCH model; the second is the iterative QML method recently proposed by Chirico (2024), which provides a volatility predictor similar to the EGARCH predictor. All three methods can also be applied in case of random-walk volatility as well as in case of Student-t distributed return innovations. Some examples illustrate the practical use of the package.