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We provide evidence that cumulative distributions of absolute normalized returns for the $100$ American companies with the highest market capitalization, uncover a critical behavior for different time scales $Delta t$. Such cumulative distributions, in accordance with a variety of complex --and financial-- systems, can be modeled by the cumulative distribution functions of $q$-Gaussians, the distribution function that, in the context of nonextensive statistical mechanics, maximizes a non-Boltzmannian entropy. These $q$-Gaussians are characterized by two parameters, namely $(q,beta)$, that are uniquely defined by $Delta t$. From these dependencies, we find a monotonic relationship between $q$ and $beta$, which can be seen as evidence of criticality. We numerically determine the various exponents which characterize this criticality.
We propose a novel approach that allows to calculate Hilbert transform based complex correlation for unevenly spaced data. This method is especially suitable for high frequency trading data, which are of a particular interest in finance. Its most imp
Data augmentation methods in combination with deep neural networks have been used extensively in computer vision on classification tasks, achieving great success; however, their use in time series classification is still at an early stage. This is ev
We test three common information criteria (IC) for selecting the order of a Hawkes process with an intensity kernel that can be expressed as a mixture of exponential terms. These processes find application in high-frequency financial data modelling.
Data normalization is one of the most important preprocessing steps when building a machine learning model, especially when the model of interest is a deep neural network. This is because deep neural network optimized with stochastic gradient descent
Many fits of Hawkes processes to financial data look rather good but most of them are not statistically significant. This raises the question of what part of market dynamics this model is able to account for exactly. We document the accuracy of such