arXiv subjects

Soledad Torres

Publications and source records attributed to Soledad Torres.

22 records · Page 2Linked to original sources

arXiv2011

Is a Brownian skew?

We study the asymptotic behavior of the maximum likelihood estimator corresponding to the observation of a trajectory of a Skew Brownian motion, through a uniform time discretization. We characterize the speed of convergence and the limiting distribution when the step size goes to zero, which in this case are non-classical, under the null hypothesis of the Skew Brownian motion being an usual Brownian motion. This allows to design a test on the skewness parameter. We show that numerical simulations that can be easily performed to estimate the skewness parameter, and provide an application in Biology.

math.PR↗

arXiv2009

Maximum likelihood estimators and random walks in long memory models

We consider statistical models driven by Gaussian and non-Gaussian self-similar processes with long memory and we construct maximum likelihood estimators (MLE) for the drift parameter. Our approach is based on the approximation by random walks of the driving noise. We study the asymptotic behavior of the estimators and we give some numerical simulations to illustrate our results.

math.ST↗

arXiv2008

Full Bayesian analysis for a class of jump-diffusion models

A new Bayesian significance test is adjusted for jump detection in a diffusion process. This is an advantageous procedure for temporal data having extreme valued outliers, like financial data, pluvial or tectonic forces records and others.

stat.ME↗

arXiv2007

Donsker theorem for the Rosenblatt process and a binary market model

In this paper, we prove a Donsker type approximation theorem for the Rosenblatt process, which is a selfsimilar stochastic process exhibiting long range dependence. By using numerical results and simulated data, we show that this approximation performs very well. We use this result to construct a binary market model driven by this process and we show that the model admits arbitrage opportunities.

math.PR↗