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This study introduces a new analytical framework for quantifying multivariate risk measures. Using the Wishart process, which is a stochastic process with values in the space of positive definite matrices, we derive several conditional tail…
We propose a generalization of the lasso that allows the model coefficients to vary as a function of a general set of modifying variables. These modifiers might be variables such as gender, age or time. The paradigm is quite general, with…
We study short-horizon forecasting in financial time series under strict causal constraints, treating the market as a non-stationary stochastic system in which any predictive observable must be computable online from information available…
Income and risk coexist, yet investors are often so focused on chasing high returns that they overlook the potential risks that can lead to high losses. Therefore, risk forecasting and risk control is the cornerstone of investment. To…
Spatially and temporally varying coefficient (STVC) models are currently attracting attention as a flexible tool to explore the spatio-temporal patterns in regression coefficients. However, these models often struggle with balancing…
We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis…
In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…
We introduce a flexible method to simultaneously infer both the drift and volatility functions of a discretely observed scalar diffusion. We introduce spline bases to represent these functions and develop a Markov chain Monte Carlo…
A new methodology has been introduced to clean the correlation matrix of single stocks returns based on a constrained principal component analysis using financial data. Portfolios were introduced, namely "Fundamental Maximum Variance…
The time-dependence of multi-point observable correlation functions are essential quantities in analysis and simulation of quantum dynamics. Open quantum systems approaches utilize two-point correlations to describe the influence of an…
Observations consisting of measurements on relationships for pairs of objects arise in many settings, such as protein interaction and gene regulatory networks, collections of author-recipient email, and social networks. Analyzing such data…
An algorithm is proposed that enables the imposition of shape constraints on regression curves, without requiring the constraints to be written as closed-form expressions, nor assuming the functional form of the loss function. This…
Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior…
The varying-coefficient model is a strong tool for the modelling of interactions in generalized regression. It is easy to apply if both the variables that are modified as well as the effect modifiers are known. However, in general one has a…
In complex systems, crucial parameters are often subject to unpredictable changes in time. Climate, biological evolution and networks provide numerous examples for such non-stationarities. In many cases, improved statistical models are…
This study introduces a data-driven, machine learning-based method to detect suitable control variables and instruments for assessing the causal effect of a treatment on an outcome in observational data. Our approach tests the joint…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
The dynamics of the equal-time cross-correlation matrix of multivariate financial time series is explored by examination of the eigenvalue spectrum over sliding time windows. Empirical results for the S&P 500 and the Dow Jones Euro Stoxx 50…
Modeling and forecasting covariance matrices of asset returns play a crucial role in finance. The availability of high frequency intraday data enables the modeling of the realized covariance matrix directly. However, most models in the…
Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to…