arXiv subjects

Karina Arias-Calluari

Publications and source records attributed to Karina Arias-Calluari.

9 recordsLinked to original sources

arXiv2025

Stylized Facts of High-Frequency Bitcoin Time Series

This paper analyses the high-frequency intraday Bitcoin dataset from 2019 to 2022. During this time frame, the Bitcoin market index exhibited two distinct periods, 2019-20 and 2021-22, characterized by an abrupt change in volatility. The Bitcoin price returns for both periods can be described by an anomalous diffusion process, transitioning from subdiffusion for short intervals to weak superdiffusion over longer time intervals. The characteristic features related to this anomalous behavior studied in the present paper include heavy tails, which can be described using a $q$-Gaussian distribution and correlations. When we sample the autocorrelation of absolute returns, we observe a power-law relationship, indicating time dependence in both periods initially. The ensemble autocorrelation of the returns decays rapidly. We fitted the autocorrelation with a power law to capture the decay and found that the second period experienced a slightly higher decay rate. The further study involves the analysis of endogenous effects within the Bitcoin time series, which are examined through detrending analysis. We found that both periods are multifractal and present self-similarity in the detrended probability density function (PDF). The Hurst exponent over short time intervals shifts from less than 0.5 ($\sim$ 0.42) in Period 1 to closer to 0.5 in Period 2 ($\sim$ 0.49), indicating that the market has gained efficiency over time.

q-fin.ST↗

arXiv2025

Assessing Honey Bee Colony Health Using Temperature Time Series

Honey bees face an increasing number of stressors that disrupt the natural behaviour of colonies and, in extreme cases, can lead to their collapse. Quantifying the status and resilience of colonies is essential to measure the impact of stressors and to identify colonies at risk. In this manuscript, we present and apply new methodologies to efficiently diagnose the status of a honey bee colony from widely available time series of hive and environmental temperature. Healthy hives have a remarkable ability to control temperature near the brood area. Our method exploits this fact and quantifies the status of a hive by measuring how resilient they are to extreme environmental temperatures, which act as natural stressors. Analysing 22 hives during different times of the year, including 3 hives that collapsed, we find the statistical signatures of stress that reveal whether honeybees are doing well or are at risk of failure. Based on these analyses, we propose a simple scale of hive status (stable, warning, and collapse) that can be determined based on a few temperature measurements. Our approach offers a lower-cost and practical bee-monitoring solution, providing a non-invasive way to track hive conditions and trigger interventions to save the hives from collapse.

stat.AP↗

arXiv2024

Comparative analysis of stationarity for Bitcoin and the S&P500

This paper compares and contrasts stationarity between the conventional stock market and cryptocurrency. The dataset used for the analysis is the intraday price indices of the S&P500 from 1996 to 2023 and the intraday Bitcoin indices from 2019 to 2023, both in USD. We adopt the definition of `wide sense stationary', which constrains the time independence of the first and second moments of a time series. The testing method used in this paper follows the Wiener-Khinchin Theorem, i.e., that for a wide sense stationary process, the power spectral density and the autocorrelation are a Fourier transform pair. We demonstrate that localized stationarity can be achieved by truncating the time series into segments, and for each segment, detrending and normalizing the price return are required. These results show that the S&P500 price return can achieve stationarity for the full 28-year period with a detrending window of 12 months and a constrained normalization window of 10 minutes. With truncated segments, a larger normalization window can be used to establish stationarity, indicating that within the segment the data is more homogeneous. For Bitcoin price return, the segment with higher volatility presents stationarity with a normalization window of 60 minutes, whereas stationarity cannot be established in other segments.

q-fin.ST↗

arXiv2023

Variable order porous media equations: Application on modeling the S&P500 and Bitcoin price return

This article reveals a specific category of solutions for the $1+1$ Variable Order (VO) nonlinear fractional Fokker-Planck equations. These solutions are formulated using VO $q$-Gaussian functions, granting them significant versatility in their application to various real-world systems, such as financial economy areas spanning from conventional stock markets to cryptocurrencies. The VO $q$-Gaussian functions provide a more robust expression for the distribution function of price returns in real-world systems. Additionally, we analyzed the temporal evolution of the anomalous characteristic exponents derived from our study, which are associated with the long-range memory in time series data and autocorrelation patterns.

cond-mat.stat-mech↗

arXiv2022

Modelling daily weight variation in honey bee hives

A quantitative understanding of the dynamics of bee colonies is important to support global efforts to improve bee health and enhance pollination services. Traditional approaches focus either on theoretical models or data-centred statistical analyses. Here we argue that the combination of these two approaches is essential to obtain interpretable information on the state of bee colonies and show how this can be achieved in the case of time series of intra-day weight variation. We model how the foraging and food processing activities of bees affect global hive weight through a set of ordinary differential equations and show how to estimate reliable ranges for the ten parameters of this model from measurements on a single day. Our analysis of 10 hives at different times shows that crucial indicators of the health of honey bee colonies are estimated robustly and fall in ranges compatible with previously reported results. The indicators include the amount of food collected (foraging success) and the number of active foragers, which may be used to develop early warning indicators of colony failure.

physics.bio-ph↗

arXiv2020

Local and Non-local Fractional Porous Media Equations

Recently it was observed that the probability distribution of the price return in S\&P500 can be modeled by $q$-Gaussian distributions, where various phases (weak, strong super diffusion and normal diffusion) are separated by different fitting parameters (Phys Rev. E 99, 062313, 2019). Here we analyze the fractional extensions of the porous media equation and show that all of them admit solutions in terms of generalized $q$-Gaussian functions. Three kinds of "fractionalization" are considered: \textit{local}, referring to the situation where the fractional derivatives for both space and time are local; \textit{non-local}, where both space and time fractional derivatives are non-local; and \textit{mixed}, where one derivative is local, and another is non-local. Although, for the \textit{local} and \textit{non-local} cases we find $q$-Gaussian solutions , they differ in the number of free parameters. This makes differences to the quality of fitting to the real data. We test the results for the S\&P 500 price return and found that the local and non-local schemes fit the data better than the classic porous media equation.

cond-mat.stat-mech↗

arXiv2020

Stationarity of the detrended price return in stock markets

This paper proposes a governing equation for stock market indexes that accounts for non-stationary effects. This is a linear Fokker-Planck equation (FPE) that describes the time evolution of the probability distribution function (PDF) of the price return. By applying Ito's lemma, this FPE is associated with a stochastic differential equation (SDE) that models the time evolution of the price return in a fashion different from the classical Black-Scholes equation. Both FPE and SDE equations account for a deterministic part or trend, and a stationary, stochastic part as a q-Gaussian noise. The model is validated using the S\&P500 index's data. After removing the trend from the index, we show that the detrended part is stationary by evaluating the Hurst exponent of the multifractal time series, its power spectrum, and its autocorrelation.

q-fin.ST↗

arXiv2020

Methods for forecasting the effect of exogenous risk on stock markets

Markets are subjected to both endogenous and exogenous risks that have caused disruptions to financial and economic markets around the globe, leading eventually to fast stock market declines. In the past, markets have recovered after any economic disruption. On this basis, we focus on the outbreak of COVID-19 as a case study of an exogenous risk and analyze its impact on the Standard and Poor's 500 (S\&P500) index. We assumed that the S\&P500 index reaches a minimum before rising again in the not-too-distant future. Here we present two cases to forecast the S\&P500 index. The first case uses an estimation of expected deaths released on 02/04/2020 by the University of Washington. For the second case, it is assumed that the peak number of deaths will occur 2-months since the first confirmed case occurred in the USA. The decline and recovery in the index were estimated for the following three months after the initial point of the predicted trend. The forecast is a projection of a prediction with stochastic fluctuations described by $q$-gaussian diffusion process with three spatio-temporal regimes. Our forecast was made on the premise that any market response can be decomposed into an overall deterministic trend and a stochastic term. The prediction was based on the deterministic part and for this case study is approximated by the extrapolation of the S\&P500 data trend in the initial stages of the outbreak. The stochastic fluctuations have the same structure as the one derived from the past 24 years. A reasonable forecast was achieved with 85\% of accuracy.

q-fin.ST↗

arXiv2018

Closed-form solutions for the Lévy-stable distribution

The Lévy-stable distribution is the attractor of distributions which hold power laws with infinite variance. This distribution has been used in a variety of research areas, for example in economics it is used to model financial market fluctuations and in statistical mechanics as a numerical solution of fractional kinetic equations of anomalous transport. This function does not have an explicit expression and no uniform solution has been proposed yet. This paper presents a uniform analytical approximation for the Lévy-stable distribution based on matching power series expansions. For this solution, the trans-stable function is defined as an auxiliary function which removes the numerical issues of the calculations of the Lévy-stable. Then, the uniform solution is proposed as a result of an asymptotic matching between two types of approximations called "the inner solution" and "the outer solution". Finally, the results of analytical approximation are compared to the numerical results of the Lévy-stable distribution function, making this uniform solution valid to be applied as an analytical approximation.

cond-mat.stat-mech↗