Related papers: Spectral estimation for diffusions with random sam…
We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class…
We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on $n$ independent replicates $\left\{X_i(t)\::\: t\in [0,1]\right\}_{1 \leq i \leq n}$, observed…
An approximate maximum likelihood method of estimation of diffusion parameters $(\vartheta,\sigma)$ based on discrete observations of a diffusion $X$ along fixed time-interval $[0,T]$ and Euler approximation of integrals is analyzed. We…
This work develops change-point methods for statistics of high-frequency data. The main interest is in the volatility of an It\^{o} semi-martingale, the latter being discretely observed over a fixed time horizon. We construct a…
Jump diffusion processes are widely used to model asset prices over time, mainly for their ability to capture complex discontinuous behavior, but inference on the model parameters remains a challenge. Here our goal is posterior inference on…
We propose a novel method for drift estimation of multiscale diffusion processes when a sequence of discrete observations is given. For the Langevin dynamics in a two-scale potential, our approach relies on the eigenvalues and the…
We consider the problem of frequency estimation by observations of the periodic diffusion process possesing ergodic properties in two different situations. The first one corresponds to continuously differentiable with respect to parameter…
We consider non-parametric Bayesian estimation of the drift coefficient of a one-dimensional stochastic differential equation from discrete-time observations on the solution of this equation. Under suitable regularity conditions that are…
This paper explores the nonparametric estimation of the volatility component in a heteroscedastic scalar-on-function regression model, where the underlying discrete-time process is ergodic and subject to a missing-at-random mechanism. We…
We study the problem of drift estimation for two-scale continuous time series. We set ourselves in the framework of overdamped Langevin equations, for which a single-scale surrogate homogenized equation exists. In this setting, estimating…
This paper presents a numerical method to implement the parameter estimation method using response statistics that was recently formulated by the authors. The proposed approach formulates the parameter estimation problem of It\^o drift…
This paper considers the problem of estimating the population spectral distribution from a sample covariance matrix in large dimensional situations. We generalize the contour-integral based method in Mestre (2008) and present a local moment…
The article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed It\^o processes in an additive microstructure noise model. In a high-frequency setting, we aim at establishing an asymptotic…
We study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current…
We consider parametric estimation and tests for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main target is to…
In the present paper, we consider that $N$ diffusion processes $X^1,\dots,X^N$ are observed on $[0,T]$, where $T$ is fixed and $N$ grows to infinity. Contrary to most of the recent works, we no longer assume that the processes are…
This article studies nonparametric methods to estimate the co-integrated volatility for multi-dimensional L\'evy processes with high frequency data. We construct a spectral estimator for the co-integrated volatility and prove minimax rates…
In the paper, the estimator for the spectral measure of multivariate stable distributions introduced by Davydov and co-workers are extended to the regularly varying distributions. The sampling method is modified to optimize the rate of…
We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and negative axis, yet discontinuous at zero. This threshold…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is discussed. A wide set of measurable quantities ("invariant moments") whose expectation value…