arXiv subjects

Jean-François Muzy

Publications and source records attributed to Jean-François Muzy.

At least 19 recordsLinked to original sources

arXiv2026

Forecasting threshold exceedance of atmospheric variables at a specific location

Accurate short-term forecasting of extreme weather events is important for early warning and risk mitigation. We compare two approaches for predicting site-specific threshold exceedances of weather variables: direct binary probabilistic models trained on thresholded outcomes and full-distribution parametric models trained on the continuous target. Using an analytically tractable Gaussian random-location model, in which the distribution is predictably shifted by the covariates, we quantify the consequences of the information loss induced by thresholding and derive the rare-event behavior of prediction errors and forecast skill. The analysis predicts an increasing relative advantage of the full-distribution approach as event probability decreases, because binarization progressively discards information contained in the continuous response. We then compare the two approaches to forecast wind speed and accumulated rainfall at various weather station sites over southeastern France using the same hybrid neural-network architecture. Although wind speed and rainfall depart from the toy-model assumptions, its main qualitative predictions are recovered for both variables: the relative advantage of distributional modeling increases toward rarer thresholds. This agreement further suggests that a substantial fraction of the forecastable signal associated with extreme events arises from predictable shifts in the conditional distribution. For the reasonably suitable parametric families examined, the results show limited sensitivity to the selected class of distribution. Overall, the results highlight the statistical advantage of training on continuous observations rather than on thresholded binary outcomes when forecasting rare threshold exceedances.

physics.ao-ph↗

arXiv2026

The Log S-fBM model: Statistical analysis

The Log S-fBM model, introduced by Wu et al., is a stochastic volatility model whose log volatility is a stationary fractional Brownian motion (S-fBM): a stationary Gaussian process with power-decaying autocovariance driven by the Hurst exponent $H$, and variance scaled by an intermittency coefficient. A key property is that it reconciles rough volatility, where $H$ is typically near $0.1$ (see Gatheral et al.), with multifractal volatility, where $H$ is close to $0$ as in Bacry, Muzy et al.: the model's volatility measure converges to a multifractal random measure as $H\to0$. Numerical findings in Wu et al. show intermittency of order $0.02$ across financial assets, motivating a small intermittency approximation of log volatility moments for calibration via the general method of moments (GMM). In this work, we conduct a statistical analysis of the Log S-fBM model. We derive scaling properties of the S-fBM process and the Log S-fBM integrated volatility measure, present deviation inequalities with tail distributions sensitive to $H$ and intermittency, and develop a hypothesis test for the null Hurst exponent, i.e.\ rough versus multifractal dynamics. Finally, we revisit scale invariance of the log volatility increment process via explicit small-intermittency formulas, reproducing analogous properties in both regimes.

q-fin.ST↗

arXiv2026

A Nested Factor Model for Equity Markets: Reconciling Multifractal Stock Returns and Rough Index Volatilities

The Nested factor model was introduced by Chicheportiche et al. to represent non-linear correlations between stocks. Stock returns are explained by a standard factor model, but the (log)-volatilities of factors and residuals are themselves decomposed into factor modes, with a common dominant volatility mode affecting both market and sector factors but also residuals. Here, we consider the case of a single factor where the only dominant log-volatility mode is rough, with a Hurst exponent $H \simeq 0.11$ and the log-volatility residuals are ''super-rough'' or ''multifractal'', with $H \simeq 0$. We demonstrate that such a construction naturally accounts for the somewhat surprising stylized fact reported by Wu et al. , where it has been observed that the Hurst exponents of stock indexes are large compared to those of individual stocks. We propose a statistical procedure to estimate the Hurst factor exponent from the stock returns dynamics together with theoretical guarantees of its consistency. We demonstrate the effectiveness of our approach through numerical experiments and apply it to daily stock data from the S&P500 index. The estimated roughness exponents for both the factor and idiosyncratic components validate the assumptions underlying our model.

q-fin.ST↗

arXiv2026

From rough to multifractal multidimensional volatility: A multidimensional Log S-fBM model

We introduce the multivariate Log S-fBM model (mLog S-fBM), extending the univariate framework proposed by Wu \textit{et al.} to the multidimensional setting. We define the multidimensional Stationary fractional Brownian motion (mS-fBM), characterized by marginals following S-fBM dynamics and a specific cross-covariance structure. It is parametrized by a correlation scale $T$, marginal-specific intermittency parameters and Hurst exponents, as well as their multidimensional counterparts: the co-intermittency matrix and the co-Hurst matrix. The mLog S-fBM is constructed by modeling volatility components as exponentials of the mS-fBM, preserving the dependence structure of the Gaussian core. We demonstrate that the model is well-defined for any co-Hurst matrix with entries in $[0, \frac{1}{2}[$, supporting vanishing co-Hurst parameters to bridge rough volatility and multifractal regimes. We generalize the small intermittency approximation technique to the multivariate setting to develop an efficient Generalized Method of Moments calibration procedure, estimating cross-covariance parameters for pairs of marginals. We validate it on synthetic data and apply it to S\&P 500 market data, modeling stock return fluctuations. Diagonal estimates of the stock Hurst matrix, corresponding to single-stock log-volatility Hurst exponents, are close to 0, indicating multifractal behavior, while co-Hurst off-diagonal entries are close to the Hurst exponent of the S\&P 500 index ($H \approx 0.12$), and co-intermittency off-diagonal entries align with univariate intermittency estimates.

q-fin.ST↗

arXiv2025

KANFormer for Predicting Fill Probabilities via Survival Analysis in Limit Order Books

This paper introduces KANFormer, a novel deep-learning-based model for predicting the time-to-fill of limit orders by leveraging both market- and agent-level information. KANFormer combines a Dilated Causal Convolutional network with a Transformer encoder, enhanced by Kolmogorov-Arnold Networks (KANs), which improve nonlinear approximation. Unlike existing models that rely solely on a series of snapshots of the limit order book, KANFormer integrates the actions of agents related to LOB dynamics and the position of the order in the queue to more effectively capture patterns related to execution likelihood. We evaluate the model using CAC 40 index futures data with labeled orders. The results show that KANFormer outperforms existing works in both calibration (Right-Censored Log-Likelihood, Integrated Brier Score) and discrimination (C-index, time-dependent AUC). We further analyze feature importance over time using SHAP (SHapley Additive exPlanations). Our results highlight the benefits of combining rich market signals with expressive neural architectures to achieve accurate and interpretabl predictions of fill probabilities.

cs.AI↗

arXiv2025

Local wind speed forecasting at short time horizons based on Numerical Weather Prediction and observations from surrounding stations

This study presents a hybrid neural network model for short-term (1-6 hours ahead) surface wind speed forecasting, combining Numerical Weather Prediction (NWP) with observational data from ground weather stations. It relies on the MeteoNet dataset, which includes data from global (ARPEGE) and regional (AROME) NWP models of the French weather service and meteorological observations from ground stations in the French Mediterranean. The proposed neural network architecture integrates recent past station observations (over last few hours) and AROME and ARPEGE predictions on a small subgrid around the target location. The model is designed to provide both deterministic and probabilistic forecasts, with the latter predicting the parameters of a suitable probability distribution that notably allows us to capture extreme wind events. Our results demonstrate that the hybrid model significantly outperforms baseline methods, including raw NWP predictions, persistence models, and linear regression, across all forecast horizons. For instance, the model reduces RMSE by up 30\% compared to AROME predictions. Probabilistic forecasting further enhances performance, particularly for extreme quantiles, by estimating conditional quantiles rather than relying solely on the conditional mean. Fine-tuning the model for specific stations, such as those in the Mediterranean island of Corsica, further improves forecasting accuracy. Our study highlights the importance of integrating multiple data sources and probabilistic approaches to improve short-term wind speed forecasting. It defines an effective approach, even in a complex terrain like Corsica where localized wind variations are significant

physics.ao-ph↗

arXiv2025

No Tick-Size Too Small: A General Method for Modelling Small Tick Limit Order Books

Tick-sizes not only influence the granularity of the price formation process but also affect market agents' behavior. We investigate the disparity in the microstructural properties of the Limit Order Book (LOB) across a basket of assets with different relative tick-sizes. A key contribution of this study is the identification of several stylized facts, which are used to differentiate between large, medium, and small-tick assets, along with clear metrics for their measurement. We provide cross-asset visualizations to illustrate how these attributes vary with relative tick-size. Further, we propose a Hawkes Process model that {\color{black}not only fits well for large-tick assets, but also accounts for }sparsity, multi-tick level price moves, and the shape of the LOB in small-tick assets. Through simulation studies, we demonstrate the {\color{black} versatility} of the model and identify key variables that determine whether a simulated LOB resembles a large-tick or small-tick asset. Our tests show that stylized facts like sparsity, shape, and relative returns distribution can be smoothly transitioned from a large-tick to a small-tick asset using our model. We test this model's assumptions, showcase its challenges and propose questions for further directions in this area of research.

q-fin.TR↗

arXiv2025

Improving prediction of heavy rainfall in the Mediterranean with Neural Networks using both observation and Numerical Weather Prediction data

Forecasting Heavy Precipitation Events (HPE) in the Mediterranean is crucial but challenging due to the complexity of the processes involved. In this context, Artificial Intelligence methods have recently proven to be competitive with state-of-the-art Numerical Weather Prediction (NWP). This work focuses on improving the prediction of the occurrence of HPE over periods from 1 h to 24 h based on Neural Network (NN) models. The proposed method uses both ground-station observations and data from Météo France's Arome and Arpege NWP models, on two regions with oceanic and Mediterranean climates for the period 2016-2018. The verification metric is the Peirce Skill Score. Results show that the NN model using only observations or NWP data performs better for shorter and longer rainfall accumulation period respectively. In contrast, a hybrid method combining both observations and NWP data offers the best performance and remains stable with the rainfall accumulation period. The hybrid method also improves the performance in predicting increasingly intense rainfall, from the 5% to the 0.1% rarest events. The choice of the loss function is found to be an important aspect of this work, where only balanced loss functions provide results insensitive to rare event frequency. Finally, the hybrid method is particularly well suited for the prediction of HPE in the Mediterranean climate, especially during the fall season, period during which most HPE occur.

physics.ao-ph↗

arXiv2024

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 consists in predicting the parameters of a given probability density function by training a neural network model whose loss function is the corresponding log-likelihood. We compare different possibilities among a set of distributions that have been previously considered in the context of modeling wind fluctuations. Our results rely on two wind datasets recorded respectively by Météo-France in Corsica (South France) and by KNMI over the Netherlands. 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 ofdistributions relies on a random cascade model model for wind speeds along the same picture as fully developed turbulence. For all stations in both regions, it consistently provides better results regardless of the considered 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 former results 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 mostly at longest time horizons ($h=6$ h). It turns out that accounting for pertinent explanatory factors, notably those related the spatial distribution and wind speed and direction, emerges as a more critical factor in enhancing accuracy than the choice of the "optimal" parametric distribution. We also find out that such explanatory factors mainly increases the resolution performances while it does not change the reliability contribution to the CRPS score.

physics.ao-ph↗

arXiv2023

Liquidity takers behavior representation through a contrastive learning approach

Thanks to the access to the labeled orders on the CAC40 data from Euronext, we are able to analyze agents' behaviors 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 utilize the K-means clustering algorithm on the learned representation vectors of agent orders to identify distinct behavior types within each cluster.

q-fin.ST↗

arXiv2023

The self-exciting nature of the bid-ask spread dynamics

The bid-ask spread, which is defined by the difference between the best selling price and the best buying price in a Limit Order Book at a given time, is a crucial factor in the analysis of financial securities. In this study, we propose a "State-dependent Spread Hawkes model" (SDSH) that accounts for various spread jump sizes and incorporates the impact of the current spread state on its intensity functions. We apply this model to the high-frequency data from the Cac40 Euronext market and capture several statistical properties, such as the spread distributions, inter-event time distributions, and spread autocorrelation functions. We illustrate the ability of the SDSH model to forecast spread values at short-term horizons.

q-fin.TR↗

arXiv2022

Leveraging data from nearby stations to improve short-term wind speed forecasts

In this paper, we address the issue of short-term wind speed prediction at a given site. We show that, when one uses spatiotemporal information as provided by wind data of neighboring stations, one significantly improves the prediction quality. Our methodology does not focus on any peculiar forecasting model but rather considers a set of various prediction methods, from a very basic linear regression to different machine learning models. In each case, our approach consists in specifically and incrementally studying the benefits of using wind data of the surrounding stations. We show that, at all horizons ranging from 1 to 6 hours ahead, the relative gain on the RMSE of the predicted wind speed can increase up to 20 %. For all the considered forecasting methods, we show that such a gain is far better than the one obtained by considering other kind of information like local weather variables or seeking for an optimal deep learning model. Moreover we provide evidence that non-linear models, as neural networks or gradient boosting methods, significantly outperform linear regression. These conclusions are simply interpreted as resulting from the ability of a method to capture the transport of the information by the main flow in the upwind direction.

physics.ao-ph↗

arXiv2022

From Rough to Multifractal volatility: the log S-fBM model

We introduce a family of random measures $M_{H,T} (d t)$, namely log S-fBM, such that, for $H>0$, $M_{H,T}(d t) = e^{ω_{H,T}(t)} d t$ where $ω_{H,T}(t)$ is a Gaussian process that can be considered as a stationary version of an $H$-fractional Brownian motion. Moreover, when $H \to 0$, one has $M_{H,T}(d t) \rightarrow {\widetilde M}_{T}(d t)$ (in the weak sense) where ${\widetilde M}_{T}(d t)$ is the celebrated log-normal multifractal random measure (MRM). Thus, this model allows us to consider, within the same framework, the two popular classes of multifractal ($H = 0$) and rough volatility ($0<H < 1/2$) models. The main properties of the log S-fBM are discussed and their estimation issues are addressed. We notably show that the direct estimation of $H$ from the scaling properties of $\ln(M_{H,T}([t, t+τ]))$, at fixed $τ$, can lead to strongly over-estimating the value of $H$. We propose a better GMM estimation method which is shown to be valid in the high-frequency asymptotic regime. When applied to a large set of empirical volatility data, we observe that stock indices have values around $H=0.1$ while individual stocks are characterized by values of $H$ that can be very close to $0$ and thus well described by a MRM. We also bring evidence that unlike the log-volatility variance $ν^2$ whose estimation appears to be poorly reliable (though used widely in the rough volatility literature), the estimation of the so-called "intermittency coefficient" $λ^2$, which is the product of $ν^2$ and the Hurst exponent $H$, appears to be far more reliable leading to values that seem to be universal for respectively all individual stocks and all stock indices.

q-fin.ST↗

arXiv2020

Sparse and low-rank multivariate Hawkes processes

We consider the problem of unveiling the implicit network structure of node interactions (such as user interactions in a social network), based only on high-frequency timestamps. Our inference is based on the minimization of the least-squares loss associated with a multivariate Hawkes model, penalized by $\ell_1$ and trace norm of the interaction tensor. We provide a first theoretical analysis for this problem, that includes sparsity and low-rank inducing penalizations. This result involves a new data-driven concentration inequality for matrix martingales in continuous time with observable variance, which is a result of independent interest and a broad range of possible applications since it extends to matrix martingales former results restricted to the scalar case. A consequence of our analysis is the construction of sharply tuned $\ell_1$ and trace-norm penalizations, that leads to a data-driven scaling of the variability of information available for each users. Numerical experiments illustrate the significant improvements achieved by the use of such data-driven penalizations.

stat.ML↗

arXiv2019

Queue-reactive Hawkes models for the order flow

In this work we introduce two variants of multivariate Hawkes models with an explicit dependency on various queue sizes aimed at modeling the stochastic time evolution of a limit order book. The models we propose thus integrate the influence of both the current book state and the past order flow. The first variant considers the flow of order arrivals at a specific price level as independent from the other one and describes this flow by adding a Hawkes component to the arrival rates provided by the continuous time Markov "Queue Reactive" model of Huang et al. Empirical calibration using Level-I order book data from Eurex future assets (Bund and DAX) show that the Hawkes term dramatically improves the pure "Queue-Reactive" model not only for the description of the order flow properties (as e.g. the statistics of inter-event times) but also with respect to the shape of the queue distributions. The second variant we introduce describes the joint dynamics of all events occurring at best bid and ask sides of some order book during a trading day. This model can be considered as a queue dependent extension of the multivariate Hawkes order-book model of Bacry et al. We provide an explicit way to calibrate this model either with a Maximum-Likelihood method or with a Least-Square approach. Empirical estimation from Bund and DAX level-I order book data allow us to recover the main features of Hawkes interactions uncovered in Bacry et al. but also to unveil their joint dependence on bid and ask queue sizes. We notably find that while the market order or mid-price changes rates can mainly be functions on the volume imbalance this is not the case for the arrival rate of limit or cancel orders. Our findings also allows us to clearly bring to light various features that distinguish small and large tick assets.

q-fin.TR↗

arXiv2018

Continuous cascades in the wavelet space as models for synthetic turbulence

We introduce a wide family of stochastic processes that are obtained as sums of self-similar localized "waveforms" with multiplicative intensity in the spirit of the Richardson cascade picture of turbulence. We establish the convergence and the minimum regularity of our construction. We show that its continuous wavelet transform is characterized by stochastic self-similarity and multifractal scaling properties. This model constitutes a stationary, "grid free", extension of $\cal W$-cascades introduced in the past by Arneodo, Bacry and Muzy using wavelet orthogonal basis. Moreover our approach generically provides multifractal random functions that are not invariant by time reversal and therefore is able to account for skewed multifractal models and for the so-called "leverage effect". In that respect, it can be well suited to providing synthetic turbulence models or to reproducing the main observed features of asset price fluctuations in financial markets.

physics.data-an↗

arXiv2018

Disentangling and quantifying market participant volatility contributions

Thanks to the access to labeled orders on the Cac40 index future provided by Euronext, we are able to quantify market participants contributions to the volatility in the diffusive limit. To achieve this result we leverage the branching properties of Hawkes point processes. We find that fast intermediaries (e.g., market maker type agents) have a smaller footprint on the volatility than slower, directional agents. The branching structure of Hawkes processes allows us to examine also the degree of endogeneity of each agent behavior. We find that high-frequency traders are more endogenously driven than other types of agents.

q-fin.TR↗

arXiv2017

Analysis of order book flows using a nonparametric estimation of the branching ratio matrix

We introduce a new non parametric method that allows for a direct, fast and efficient estimation of the matrix of kernel norms of a multivariate Hawkes process, also called branching ratio matrix. We demonstrate the capabilities of this method by applying it to high-frequency order book data from the EUREX exchange. We show that it is able to uncover (or recover) various relationships between all the first level order book events associated with some asset when mapped to a 12-dimensional process. We then scale up the model so as to account for events on two assets simultaneously and we discuss the joint high-frequency dynamics.

q-fin.TR↗