Ernesto Mordecki

Argimiro Arratia, Alejandra Cabaña, Ernesto Mordecki et al.

Model selection in non-linear models often prioritizes performance metrics over statistical tests, limiting the ability to account for sampling variability. We propose the use of a statistical test to assess the equality of variances in forecasting errors. The test builds upon the classic Morgan-Pitman approach, incorporating enhancements to ensure robustness against data with heavy-tailed distributions or outliers with high variance, plus a strategy to make residuals from machine learning models statistically independent. Through a series of simulations and real-world data applications, we demonstrate the test's effectiveness and practical utility, offering a reliable tool for model evaluation and selection in diverse contexts.

E. Mordecki, A. Szepessy, R. Tempone et al.

This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational error, with computable leading order term in a posteriori form, based on stochastic flows and discrete dual backward problems which extends the results in [STZ]. These expansions lead to efficient and accurate computation of error estimates. Adaptive algorithms for either stochastic time steps or quasi-deterministic time steps are described. Numerical examples show the performance of the proposed error approximation and of the described adaptive time-stepping methods.