Our goal in this work is to construct empirical confidence intervals for the fractional parameter d in ARFIMA(0, d, 0) processes. Through these confidence intervals one can compare several estimators for d to decide which one is the best estimation method related to long memory time series. We use a fortran routine that simulates random time series to latter perform an analysis for detecting lo...

Many geophysical quantities, such as atmospheric temperature, water levels in rivers, and wind speeds, have shown evidence of long memory (LM). LM implies that these quantities experience non-trivial temporal memory, which potentially not only enhances their predictability, but also hampers the detection of externally forced trends. Thus, it is important to reliably identify whether or not a sy...

In this paper, we discuss two distinct multivariate time series models that extend the univariate ARFIMA model. We describe algorithms for computing the covariances of each model, for computing the quadratic form and approximating the determinant for maximum likelihood estimation, and for simulating from each model. We compare the speed and accuracy of each algorithm to existing methods and mea...

In this paper, we have examined 4 models for Great Salt Lake level forecasting: ARMA (Auto-Regression and Moving Average), ARFIMA (Auto-Regressive Fractional Integral and Moving Average), GARCH (Generalized Auto-Regressive Conditional Heteroskedasticity) and FIGARCH (Fractional Integral Generalized Auto-Regressive Conditional Heteroskedasticity). Through our empirical data analysis where we div...

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau...

The R/S test has been extensively used in testing the long memory of financial time series, but little attentions have been paid on its validity. The paper sets the chemical raw materials styrene price time series as an example, to test the stable of the price series. It indicates that we should give prudent explanation for the R/S test, and then establish the ARFIMA model to determine the data...

This paper presents a brief overview of some existing fractional order signal processing (FOSP) techniques where the developments in the mathematical communities are introduced; relationship between the fractional operator and long-range dependence is demonstrated, and fundamental properties of each technique and some of its applications are summarized. Specifically, we presented a tutorial on ...

A number of recent papers have suggested that the series of time intervals produced in continuation tapping may have fractal properties. This proposition, nevertheless, was only based on the visual appraisal of graphical results, and was not statistically supported. In the present study, we applied the ARMA/ARFIMA modeling procedures proposed by Wagenmakers, Farrell, and Ratcliff (2005) to test...