Linear processes in high-dimension: phase space and critical properties

In this work we investigate the generic properties of a stochastic linear model in the regime of high-dimensionality. We consider in particular the Vector AutoRegressive model (VAR) and the multivariate Hawkes process. We analyze both deterministic and random versions of these models, showing the existence of a stable and an unstable phase. We find that along the transition region separating the two regimes, the correlations of the process decay slowly, and we characterize the conditions under which these slow correlations are expected to become power-laws. We check our findings with numerical simulations showing remarkable agreement with our predictions. We finally argue that real systems with a strong degree of self-interaction are naturally characterized by this type of slow relaxation of the correlations.Comment: 40 pages, 5 figure

Improving probabilistic wind speed forecasting using M-Rice distribution and spatial data integration

We consider the problem of short-term forecasting of surface wind speed probability distribution. Our approach simply consists in predicting the parameters of a probability density function by training a neural network model whose loss function is the log-likelihood provided by this distribution. We compare different possibilities among a set of laws that have been previously considered in the context of modeling wind fluctuations. Our results rely on two different hourly wind speed datasets: the first one has been recorded by M\'et\'eo-France in Corsica (South France), a very mountainous Mediterranean island while the other one relies on KNMI database that provides records of various stations over the Netherlands, a very flat country in Northwestern Europe. A first part of our work globally unveils the superiority of the so-called "Multifractal Rice" (M-Rice) distribution over alternative parametric models, showcasing its potential as a reliable tool for wind speed forecasting. This family of distributions has been proposed in the context of modeling wind speed fluctuations as a random cascade model. For all stations in both regions, it consistently provides better results regardless the considered probabilistic scoring rule or forecasting horizon. Our second findings demonstrate significant enhancements in forecasting accuracy when one incorporates wind speed data from proximate weather stations, in full agreement with the results obtained formerly for point-wise wind speed prediction. Moreover, we reveal that the incorporation of ERA5 reanalysis of 10 m wind data from neighboring grid points contributes to a substantial improvement at time horizon $h=6$ hours. We also find out that accounting for more explanatory factors mainly increases the resolution performances while it does not change the reliability contribution to the prediction performance metric considered (CRPS).Comment: 31 pages, 8 figures, 11 table

Intermittent process analysis with scattering moments

Scattering moments provide nonparametric models of random processes with stationary increments. They are expected values of random variables computed with a nonexpansive operator, obtained by iteratively applying wavelet transforms and modulus nonlinearities, which preserves the variance. First- and second-order scattering moments are shown to characterize intermittency and self-similarity properties of multiscale processes. Scattering moments of Poisson processes, fractional Brownian motions, L\'{e}vy processes and multifractal random walks are shown to have characteristic decay. The Generalized Method of Simulated Moments is applied to scattering moments to estimate data generating models. Numerical applications are shown on financial time-series and on energy dissipation of turbulent flows.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1276 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Agent market orders representation through a contrastive learning approach

Due to the access to the labeled orders on the CAC40 data from Euronext, we are able to analyse agents' behaviours in the market based on their placed orders. In this study, we construct a self-supervised learning model using triplet loss to effectively learn the representation of agent market orders. By acquiring this learned representation, various downstream tasks become feasible. In this work, we utilise the K-means clustering algorithm on the learned representation vectors of agent orders to identify distinct behaviour types within each cluster

Modelling microstructure noise with mutually exciting point processes

International audienceWe introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point pro- cesses and relies on linear self and mutually exciting stochastic inten- sities as introduced by Hawkes. We associate a counting process with the positive and negative jumps of an asset price. By coupling suitably the stochastic intensities of upward and downward changes of prices for several assets simultaneously, we can reproduce microstructure noise (i.e. strong microscopic mean reversion at the level of seconds to a few minutes) and the Epps effect (i.e. the decorrelation of the increments in microscopic scales) while preserving a standard Brownian diffusion behaviour on large scales. More effectively, we obtain analytical closed-form formulae for the mean signature plot and the correlation of two price increments that enable to track across scales the effect of the mean-reversion up to the diffusive limit of the model. We show that the theoretical results are consistent with empirical fits on futures Euro-Bund and Euro-Bobl in several situations