Modelling financial time series with SEMIFAR–GARCH model

A class of semiparametric fractional autoregressive models with generalized autoregressive conditional heteroskedastic (GARCH) errors, which includes deterministic trends, difference stationarity and stationarity with short- and long-range dependence and heteroskedastic model errors, is very powerful for modelling financial time series. This paper discusses the model fitting, including an efficient algorithm and parameter estimation of GARCH error term, so that the model can be applied in practice. We then illustrate the model and estimation methods with a few of different finance data sets.