Related papers: Maximum likelihood type estimation for discretely …
Consider an estimation of the Hurst parameter $H\in(0,1)$ and the volatility parameter $\sigma>0$ for a fractional Brownian motion with a drift term under high-frequency observations with a finite time interval. In the present paper, we…
In this paper, we develop econometric tools to analyze the integrated volatility of the efficient price and the dynamic properties of microstructure noise in high-frequency data under general dependent noise. We first develop consistent…
We discuss maximum likelihood estimation of parameters for models governed by a stochastic differential equation driven by a mixed fractional Brownian motion with random effects.
The question of the volatility roughness is interpreted in the framework of a data-reconstructed fractional volatility model, where volatility is driven by fractional noise. Some examples are worked out and also, using Malliavin calculus…
Based on a criterium of mathematical simplicity and consistency with empirical market data, a stochastic volatility model has been obtained with the volatility process driven by fractional noise. Depending on whether the stochasticity…
Rough volatility models have gained considerable interest in the quantitative finance community in recent years. In this paradigm, the volatility of the asset price is driven by a fractional Brownian motion with a small value for the Hurst…
We study the distribution of maxima (Extreme Value Statistics) for sequences of observables computed along orbits generated by random transformations. The underlying, deterministic, dynamical system can be regular or chaotic. In the former…
In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…
Recently, various algorithms for data-driven simulation and control have been proposed based on the Willems' fundamental lemma. However, when collected data are noisy, these methods lead to ill-conditioned data-driven model structures. In…
We consider discrete graphical models Markov with respect to a graph $G$ and propose two distributed marginal methods to estimate the maximum likelihood estimate of the canonical parameter of the model. Both methods are based on a…
AIMS. The maximum-likelihood method is the standard approach to obtain model fits to observational data and the corresponding confidence regions. We investigate possible sources of bias in the log-likelihood function and its subsequent…
This paper is concerned with a new optimization problem named "phase change rate maximization" for single-input-single-output linear time-invariant systems. The problem relates to two control problems, namely robust instability analysis…
A parameter estimation problem is considered for a diagonaliazable stochastic evolution equation using a finite number of the Fourier coefficients of the solution. The equation is driven by additive noise that is white in space and…
We consider a stochastic differential equation of the form \[dX_t=\theta a(t,X_t)\,dt+\sigma_1(t,X_t)\sigma_2(t,Y_t)\,dW_t\] with multiplicative stochastic volatility, where $Y$ is some adapted stochastic process. We prove…
The notions of noise sensitivity and stability were recently extended for the voter model. In this model, the vertices of a graph have opinions that are updated by uniformly selecting edges. We further extend stability results to different…
We consider a dissipative vector field which is represented by a nearly-integrable Hamiltonian flow to which a non symplectic force is added, so that the phase space volume is not preserved. The vector field depends upon two parameters,…
We consider statistical inference for a class of dynamic mixed-effect models described by stochastic differential equations whose drift and diffusion coefficients simultaneously depend on fixed- and random-effect parameters. Assuming that…
Linear structural equation models postulate noisy linear relationships between variables of interest. Each model corresponds to a path diagram, which is a mixed graph with directed edges that encode the domains of the linear functions and…
The paper deals with the regression model $X_t = \theta t + B_t$, $t\in[0, T ]$, where $B=\{B_t, t\geq 0\}$ is a centered Gaussian process with stationary increments. We study the estimation of the unknown parameter $\theta$ and establish…
For the Ornstein-Uhlenbeck process, the asymptotic behavior of the maximum likelihood estimator of the drift parameter is totally different in the stable, unstable, and explosive cases. Notwithstanding of this trichotomy, we investigate…