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The Edwards-Wilkinson (EW) growth of $1+1$ interface is considered in the background of the correlated random noise. We use random Coulomb potential as the background long-range correlated noise. A depinning transition is observed in a…
This note discusses some of the aspects of a model for the covariance of equity returns based on a simple "isotropic" structure in which all pairwise correlations are taken to be the same value. The effect of the structure on feasible…
This thesis applies entropy as a model independent measure to address three research questions concerning financial time series. In the first study we apply transfer entropy to drawdowns and drawups in foreign exchange rates, to study their…
Transformer models have become increasingly popular in financial applications, yet their potential risk making and biases remain under-explored. The purpose of this work is to audit the reliance of the model on volatile data for…
In multi-condition EEG experiments, brain activity is recorded as subjects perform various tasks or are exposed to different stimuli. The recorded signals are commonly transformed into time-frequency representations, which often display…
We discuss intermittent time series consisting of discrete bursts or avalanches separated by waiting or silent times. The short time correlations can be understood to follow from the properties of individual avalanches, while longer time…
Positional encodings are essential to transformer-based generative models, yet their behavior in multimodal and attention-sharing settings is not fully understood. In this work, we present a principled analysis of Rotary Positional…
In Financial Signal Processing, multiple time series such as financial indicators, stock prices and exchange rates are strongly coupled due to their dependence on the latent state of the market and therefore they are required to be jointly…
This paper studies the estimation of linear panel data models with interactive fixed effects, where one dimension of the panel, typically time, may be fixed. To this end, a novel transformation is introduced that reduces the model to a…
We investigate the behavior of correlations dynamics in a dissipative gain-loss system. First, we consider a setup made of two coupled lossy oscillators, with one of them subject to a local gain. This provides a more realistic platform to…
Fluctuations in stock prices are influenced by a complex interplay of factors that go beyond mere historical data. These factors, themselves influenced by external forces, encompass inter-stock dynamics, broader economic factors, various…
This paper shows that jumps in financial asset prices are often erroneously identified and are, in fact, rare events accounting for a very small proportion of the total price variation. We apply new econometric techniques to a comprehensive…
In the era of proliferation of large language and image generation models, the phenomenon of "model collapse" refers to the situation whereby as a model is trained recursively on data generated from previous generations of itself over time,…
We present a general approach for studying autoregressive categorical time series models with dependence of infinite order and defined conditional on an exogenous covariate process. To this end, we adapt a coupling approach, developed in…
Poisson distributed measurements in inverse problems often stem from Poisson point processes that are observed through discretized or finite-resolution detectors, one of the most prominent examples being positron emission tomography (PET).…
We consider the model of random sequential adsorption, with depositing objects, as well as those already at the surface, decreasing in size according to a specified time dependence, from a larger initial value to a finite value in the large…
Long-lived beatings in two-dimensional electronic spectroscopy (2DES) remain difficult to interpret within standard excitonic open-system models, which typically assume factorized initialization and predict rapid coherence decay. We show…
We study the dynamics of the linear and non-linear serial dependencies in financial time series in a rolling window framework. In particular, we focus on the detection of episodes of statistically significant two- and three-point…
We prove regenerative properties for the linear Hawkes process under minimal assumptions on the transfer function, which may have unbounded support. These results are applicable to sliding window statistical estimators. We exploit…
A new form of two-photon exchange(TPE) effect is studied to explain the discrepancy between unpolarized and polarized experimental data in elastic $ep$ scattering. The mechanism is based on a simple idea that apart from the usual TPE…