Superstatistics with cut-off tails for financial time series

Uchiyama, Yusuke; Kadoya, Takanori

doi:10.1016/j.physa.2019.04.166

Cited by 6 publications

(5 citation statements)

References 35 publications

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“…In a subjective probability perspective of complex systems, the notion of mixed renewal processes is related to the concept of superstatistics, which indicates a superposition of several statistics on different scales [43,72]. A superstatistical interpretation of renewal processes has been applied in various fields, including financial markets, traffic delays, air pollution dynamics and hydrodynamic turbulence [73][74][75][76]. A future research direction will be the development of a event-sequence technique which may detect the presence of memory between the events through the effect of renewal aging.…”

Section: Discussionmentioning

confidence: 99%

Aging Renewal Point Processes and Exchangeability of Event Times

Vanni,

Lambert

2024

Preprint

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We investigate the impact of aging on exchangeable inter-arrival times in mixed renewal processes, exploring its implications for reliability and survival analysis. In this study, first, we revisit the definition of renewal point processes, where inter-event time intervals are considered as exchangeable non-negative random variables. Then, we define the concept of statistical aging as latency in the observational process of event counting. Latency affects event detection but preserves exchangeability. However, it may alter the statistical properties of inter-event time intervals. Our analytical and numerical assessments highlight the significance of aging in exchangeable lifetimes, offering insights into key metrics such as the failure survival function, renewal function, and hazard rate function. Through archetypal examples and empirical findings, we illustrate the implications of aging on renewal processes. In particular, employing a Bayesian perspective, we analyze high-frequency currency exchange rate data to assess the impact of aging on volatility risk evaluation. This study contributes novel insights to the literature of renewal theory and survival analysis, emphasizing the role of latency aging in stochastic point processes under exchangeability assumption.

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Section: Discussionmentioning

confidence: 99%

Aging Renewal Point Processes and Exchangeability of Event Times

Vanni,

Lambert

2024

Preprint

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“…In a subjective probability perspective of complex systems, the notion of mixed renewal processes is related to the concept of superstatistics, which indicates a superposition of several statistics on different scales [82,83]. A superstatistical interpretation of renewal processes has been applied in various fields, including financial markets, traffic delays, air pollution dynamics, and hydrodynamic turbulence [84][85][86][87]. In future work, we would like to establish a connection between the concept of superstatisics and the phenomenon of persistence within the realm of non-equilibrium statistical mechanics.…”

Section: Discussionmentioning

confidence: 99%

Aging Renewal Point Processes and Exchangeability of Event Times

Vanni,

Lambert

2024

Mathematics

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In this paper, we investigate the impact of latency aging on exchangeable (invariant under permutation of indices) inter-arrival times arising from mixed renewal point processes (statistical mixtures of point processes with renewal inter-arrival times) and explore the implications for reliability and survival analysis. We prove that aging preserves the exchangeability of inter-arrival times. Our data analysis, which includes both surrogate data and a Bayesian approach to high-frequency currency exchange-rate data, shows how aging impacts key survival analysis metrics such as failure survival, renewal, and hazard rate functions.

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“…A given time series is then said to follow a χ 2 , an inverse χ 2 or a log-normal superstatistics, depending on what the actual distribution of β is. As superstatistics was originally derived for temperature fluctuations, β is often interpreted as an inverse temperature [22], related to the local kinetic energy in the system. But in general it is just a fluctuating inverse variance parameter of a given time series.…”

Section: Superstatistical Time Series Analysismentioning

confidence: 99%

“…Originating in turbulence modelling [3], superstatistics has been applied to many physical systems, such as plasma physics [4,5], Ising systems [6], cosmic ray physics [7,8], self-gravitating systems [9], solar wind [10], high energy scattering processes [11][12][13], ultracold gases [14] and non-Gaussian diffusion processes in small complex systems [15,16]. Furthermore, the framework has successfully been applied to completely different areas, such as modelling the power-grid frequency [17], wind statistics [18], air pollution [19], bacterial DNA [20], financial time series [21,22], rain fall statistics [23] or train delays [24]. The overview article [25] provides a recent introduction to superstatistics and non-Gaussian diffusion.…”

Section: Introductionmentioning

confidence: 99%

Fluctuations of water quality time series in rivers follow superstatistics

Schafer¹,

Heppell²,

Rhys³

et al. 2021

Preprint

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Superstatistics is a general method from nonequilibrium statistical physics which has been applied to a variety of complex systems, ranging from hydrodynamic turbulence to traffic delays and air pollution dynamics. Here, we investigate water quality time series (such as dissolved oxygen concentrations and electrical conductivity) as measured in rivers, and provide evidence that they exhibit superstatistical behaviour. Our main example are time series as recorded in the river Chess in South East England. Specifically, we use seasonal detrending and empirical mode decomposition (EMD) to separate trends from fluctuations for the measured data. With either detrending method, we observe heavy-tailed fluctuation distributions, which are well described by a log-normal superstatistics for dissolved oxygen. Contrarily, we find a double peaked non-standard superstatistics for the electrical conductivity data, which we model using two combined χ 2 -distributions.

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Superstatistics with cut-off tails for financial time series

Cited by 6 publications

References 35 publications

Aging Renewal Point Processes and Exchangeability of Event Times

Aging Renewal Point Processes and Exchangeability of Event Times

Aging Renewal Point Processes and Exchangeability of Event Times

Fluctuations of water quality time series in rivers follow superstatistics

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