We discuss computational aspects of likelihood-based estimation of univariate ARFIMA(p, d, q) models. We show how efficient computation and simulation is feasible, even for large samples. We also discuss the implementation of analytical bias corrections.

A new parametric minimum distance time-domain estimator for ARFIMA processes is introduced in this paper. The proposed estimator minimizes the sum of squared correlations of residuals obtained after filtering a series through ARFIMA parameters. The estimator is easy to compute and is consistent and asymptotically normally distributed for fractionally integrated (FI) processes with an integratio...

In this paper, we use wavelet analysis to localize in Paris, France, a mean-reverting Ornstein-Uhlenbeck process with seasonality in the level and volatility. Wavelet analysis is an extension of the Fourier transform, which is very well suited to the analysis of non-stationary signals. We use wavelet analysis to identify the seasonality component in the temperature process as well as in the vol...

The purpose of this paper is to consider how to forecast implied volatility for a selection of UK companies with traded options on their stocks. We consider a range of GARCH and logARFIMA based models as well as some simple forecasting rules. Overall, we find that a logARFIMA model forecasts best over short and long horizons. Key-words : Implied Volatility, Forecasting, ARFIMA, GARCH, log-ARFIM...

This paper introduces a family of “generalized long-memory time series models”, in which observations have a specified conditional distribution, given a latent Gaussian fractionally integrated autoregressive moving average (ARFIMA) process. The observations may have discrete or continuous distributions (or a mixture of both). The family includes existing models such as ARFIMA models themselves,...