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,...

In the last decade, several HRV based novel methodologies for describing and assessing heart rate dynamics have been proposed in the literature with the aim of risk assessment. Such methodologies attempt to describe the non-linear and complex characteristics of HRV, and hereby the focus is in two of these characteristics, namely long memory and heteroscedasticity with variance clustering. The A...

We develop an easy-to-implement method for forecasting a stationary autoregressive fractionally integrated moving average (ARFIMA) process subject to structural breaks with unknown break dates. We show that an ARFIMA process subject to a mean shift and a change in the long memory parameter can be well approximated by an autoregressive (AR) model and suggest using an information criterion (AIC o...

in this paper we investigate the long memory of tehran securities price index and fit arfima model using 970 daily data since 1382/1/6 until 1386/4/17. furthermore, we compare the forecasting performance of arfima and arima models. the results show that the series is a long memory one and therefore it can become stationary by fractional differencing. we obtaine the fractional differencing param...