Long-range dependence in the volatility of returns in Uruguayan sovereign debt indices

Abstract

One consequence of the fact that a large number of agents with different behaviors operate in financial systems is the emergence of certain statistical properties in some time series. Some of these properties contradict the hypotheses that are established in the traditional models of efficient market and portfolio optimization. Among them is the long-range dependence that is the objective of this work. The approach is proposed by fractional calculus, as a generalization of the classic approach to financial markets through semi-martingales. This paper study the existence of this property in variables dependent on the term structure curves of Uruguayan sovereign debt after the 2002 economic crisis.

Particulate matter 10 (PM10): persistence and trends in eight European capitals

“…Long memory is a feature of time series that are characterised by a high degree of dependence between observations which are far apart in time. It has been found to be displayed by many time series in different fields such as climatology (Gil-Alana 2005, 2008Vyushin and Kushner 2009;Franzke 2012;Ludescher et al 2016;Bunde 2017;Yuan et al 2019;Bruneau et al 2020), environmental sciences (Barros et al 2016;Gil-Alana et al 2016;Tiwari et al 2016;Solarin 2018, Gil-Alana andTrani 2019;Xayasouk et al 2020) and economics and finance (Gil-Alana and Moreno 2012;Abritti et al 2017;Kalemkerian and Sosa 2020;Murialdo et al 2020;Qiu et al 2020).…”

Multi-mixed fractional Brownian motions and Ornstein–Uhlenbeck processes

“…The increments of fBm are a well-known stationary process, that is long-range dependent (LRD) if H > 1/2, see [18]. Motivated by this, we consider the LRD for the increments of the mmfBm…”

“…where 0 = c ∈ R, and "∼" means the ratio of left and right sides tends to 1, is called long-range dependent (having long memory) if 0 < α ≤ 1, and short-range dependent (having short memory) if α > 1, see [18].…”

Time trends and persistence in PM2.5 in 20 megacities: evidence for the time period 2018–2020

“…Long memory is an aspect of the time series where the high degree of dependence between indicators that are widely separated in time stands out. Analysing the bibliography on this methodology, we find that it has been used in many areas of knowledge, for example in the economic-financial field (Gil-Alana and Moreno 2012; Abritti et al 2017;Kalemkerian and Sosa 2020;Murialdo et al 2020;Qiu et al 2020); in the tourism sector (Al-Shboul and Anwar 2017; Pérez-Rodríguez and Santana-Gallego 2020), as well as in climatology and environmental sciences (Gil-Alana 2005, 2008Vyushin and Kushner 2009;Franzke 2012;Ludescher et al 2016;Barros et al 2016;Tiwari et al 2016;Bunde 2017;Yuan et al 2019;Gil-Alana and Solarin 2018;Gil-Alana and Trani 2019;Bruneau et al 2020;Gil-Alana et al 2020a, b;Xayasouk et al 2020;Yaya et al 2020). In this latter area, the most recent writing using fractional integration is that of Caporale et al (2021).…”