In this survey paper we present a systematic methodology which demonstrates how to
identify the origins of fractional dynamics. We consider three mechanisms which lead to it …

Fractional Brownian motion (FBM) is related to the notions of self-similarity, ergodicity and
long memory. These properties have made FBM important in modeling real-world …

This paper is devoted to testing time series that exhibit behavior related to two or more
regimes with different statistical properties. Motivation of our study are two real data sets …

In this paper we present an identification and validation scheme for stable autoregressive
fractionally integrated moving average (ARFIMA) time series. The identification part relies on …

In this paper, we extend a method of estimation of parameters of the fractional
autoregressive integrated moving average (FARIMA) process with stable noise to the case …

We construct a momentum factor that identifies cross-sectional winners and losers based on
a weighting scheme that incorporates all the price data, over the entire lookback period, as …

This paper addresses an important problem of modeling and prediction of phenomena with
antipersistent behavior and variance changing in time. As a proper stochastic model we …

We show how to use a fractional autoregressive integrated moving average (FARIMA)
model to a statistical analysis of the subdiffusive dynamics. The discrete time FARIMA (1, d …

Abstract Golding and Cox (Phys. Rev. Lett., 96 (2006) 098102) tracked the motion of
individual fluorescently labelled mRNA molecules inside live E. coli cells. They found that in …

In this article, we concentrate on modelling heavy-tailed data which can be subjected to left-
truncation. We modify an existing procedure for modelling left-truncated data via a …