This paper revisits the topic of time-scale parameterizations of the Heston-Nandi GARCH (1,1) model to create a new, theoretically valid setting compatible with real financial data. We first estimate parameters using three US market indices and six frequencies to let data reveal the correct,...

We extend the fractionally integrated exponential GARCH (FIEGARCH) model for daily stock return data with long memory in return volatility of Bollerslev and Mikkelsen (1996) by introducing a possible volatility-in-mean effect. To avoid that the long memory property of volatility carries over to...

We consider the properties of three estimation methods for integrated volatility, i.e. realized volatility, the Fourier estimator, and the wavelet estimator, when a typical sample of high-frequency data is observed. We employ several different generating mechanisms for the instantaneous...