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Volatility measures the amplitude of price fluctuations. Despite it is one of the most important quantities in finance, volatility is not directly observable. Here we apply a maximum likelihood method which assumes that price and volatility…

Computational Finance · Quantitative Finance 2012-09-03 Jordi Camprodon , Josep Perelló

We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with non-Gaussian $\alpha$-stable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the…

Statistics Theory · Mathematics 2009-08-14 Beth Andrews , Matthew Calder , Richard A. Davis

We estimate the Hurst parameter $H \in (0,1)$ of a fractional Brownian motion from discrete noisy data, observed along a high frequency sampling scheme. When the intensity $\tau_n$ of the noise is smaller in order than $n^{-H}$ we establish…

Statistics Theory · Mathematics 2022-05-27 Grégoire Szymanski

The aim of this paper is to study the asymptotic properties of the maximum likelihood estimator (MLE) of the drift coefficient for fractional stochastic heat equation driven by an additive space-time noise. We consider the traditional for…

Probability · Mathematics 2019-04-25 Igor Cialenco , Francisco Delgado-Vences , Hyun-Jung Kim

This paper deals with the problems of consistence and strong consistence of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. A central limit theorem for…

Statistics Theory · Mathematics 2009-04-28 Hu Yaozhong , Xiao Weilin , Zhang Weiguo

We prove the strong consistency and the asymptotic normality of the maximum likelihood estimator of the parameters of a general conditionally heteroscedastic model with $\alpha$-stable innovations. Then, we relax the assumptions and only…

Statistics Theory · Mathematics 2013-01-01 Guillaume Lepage

We consider a microstructure model for a financial asset, allowing for price discreteness and for a diffusive behavior at large sampling scale. This model, introduced by Delattre and Jacod, consists in the observation at the high frequency…

Statistics Theory · Mathematics 2009-09-07 Mathieu Rosenbaum

We study the problem of parametric estimation for continuously observed stochastic processes driven by additive small fractional Brownian motion with Hurst index 0<H<1/2 and 1/2<H<1. Under some assumptions on the drift coefficient, we…

Statistics Theory · Mathematics 2022-01-04 Shohei Nakajima , Yasutaka Shimizu

We study the maximum likehood estimator and least squares estimator for drift parameters of nonlinear reflected stochastic differential equations based on continuous observations. Under some regular conditions, we obtain the consistency and…

Statistics Theory · Mathematics 2022-05-04 Han Yuecai , Zhang Dingwen

We study asymptotic properties of maximum likelihood estimators of drift parameters for a jump-type Heston model based on continuous time observations, where the jump process can be any purely non-Gaussian L\'evy process of not necessarily…

Statistics Theory · Mathematics 2018-06-08 Matyas Barczy , Mohamed Ben Alaya , Ahmed Kebaier , Gyula Pap

The mixed fractional Vasicek model, which is an extended model of the traditional Vasicek model, has been widely used in modelling volatility, interest rate and exchange rate. Obviously, if some phenomenon are modeled by the mixed…

Probability · Mathematics 2020-07-16 Chunhao Cai , Yinzhong Huang , Weilin Xiao

The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…

Statistics Theory · Mathematics 2018-01-31 Marie Turčičová , Jan Mandel , Kryštof Eben

This paper deals with the maximum likelihood estimator for the mean-reverting parameter of a first order autoregressive models with exogenous variables, which are stationary Gaussian noises (Colored noise). Using the method of the Laplace…

Statistics Theory · Mathematics 2020-11-19 Chunhao Cai

We investigate the parameter estimation and prediction of two forms of the stochastic SIR model driven by small L\'{e}vy noise with time-dependent periodic transmission. We present consistency and rate of convergence results for the…

Statistics Theory · Mathematics 2024-04-24 Terry Easlick , Wei Sun

We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an…

Statistics Theory · Mathematics 2015-03-19 Markus Bibinger , Markus Reiß

We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small L\'{e}vy noises. We do not impose any moment condition on the driving L\'{e}vy process. Under certain regularity conditions…

Statistics Theory · Mathematics 2012-05-23 Hongwei Long , Yasutaka Shimizu , Wei Sun

We consider the parametric estimation of the volatility and jump activity in a stable Cox-Ingersoll-Ross ($\alpha$-stable CIR) model driven by a standard Brownian Motion and a non-symmetric stable L\'evy process with jump activity $\alpha…

Statistics Theory · Mathematics 2024-08-01 Elise Bayraktar , Emmanuelle Clément

We consider the problem of optimal estimation of the value of a vector parameter $\thetavector=(\theta_0,\ldots,\theta_n)^{\top}$ of the drift term in a fractional Brownian motion represented by the finite sum…

Statistics Theory · Mathematics 2017-07-25 A. V. Artemov , E. V. Burnaev

Generative models that maximize model likelihood have gained traction in many practical settings. Among them, perturbation based approaches underpin many strong likelihood estimation models, yet they often face slow convergence and limited…

Information Theory · Computer Science 2025-10-27 Yirong Shen , Lu Gan , Cong Ling

We propose an update estimation method for a diffusion parameter from high-frequency dependent data under a nuisance drift element. We ensure the asymptotic equivalence of the estimator to the corresponding quasi-MLE, which has the…

Statistics Theory · Mathematics 2015-06-30 Yusuke Shimizu