A class of semiparametric fractional autoregressive GARCH models (SEMIFARGARCH), 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...

Nonparametric regression with long-range and antipersistent errors is considered. Local polynomial smoothing is investigated for the estimation of the trend function and its derivatives. It is well known that in the presence of long memory (with a fractional differencing parameter 0 d 1/2),...

The distinction between stationarity, difference stationarity, deterministic trends as well as between short- and long-range dependence has a major impact on statistical conclusions, such as confidence intervals for population quantities or point and interval forecasts. In this paper, recent...

This paper considers simultaneous modelling of seasonality, slowly changing un- conditional variance and conditional heteroskedasticity in high-frequency financial returns. A new approach, called a seasonal SEMIGARCH model, is proposed to perform this by introducing multiplicative seasonal and...

Filtered log-periodogram regression estimation of the fractional differencing parameter d is considered. Asymptotic properties are derived and the effect of filtering on ˆ d is investigated. It is shown that the estimator by Geweke and Porter-Hudak (1983) can be improved significantly using a...

In this paper data-driven algorithms for fitting SEMIFAR models (Beran, 1999) are proposed. The algorithms combine the data-driven estimation of the nonparametric trend and maximum likelihood estimation of the parameters. For selecting the bandwidth, the proposal of Beran and Feng (1999) based...

This paper proposes a semiparametric approach by introducing a smooth scale function into the standard GARCH model so that conditional heteroskedasticity and scale change in a financial time series can be modelled simultaneously. An estimation procedure combining kernel estimation of the scale...