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In this article, we study the limit distribution of the least square estimator, properly normalized, from a regression model in which observations are assumed to be finite ($\alpha N$) and sampled under two different random times. Based on…

Statistics Theory · Mathematics 2020-12-17 Tania Roa , Soledad Torres , Ciprian tudor

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…

Statistics Theory · Mathematics 2022-06-13 Tetsuya Takabatake

A non-parametric diffusion model with an additive fractional Brownian motion noise is considered in this work. The drift is a non-parametric function that will be estimated by two methods. On one hand, we propose a locally linear estimator…

Probability · Mathematics 2014-03-13 Bruno Saussereau

A continuous-time regression model with a jointly strictly sub-Gaussian random noise is considered in the paper. Upper exponential bounds for probabilities of large deviations of the least squares estimator for the regression parameter are…

Probability · Mathematics 2018-06-12 Alexander V. Ivanov , Igor V. Orlovskyi

In this note a new high performance least squares parameter estimator is proposed. The main features of the estimator are: (i) global exponential convergence is guaranteed for all identifiable linear regression equations; (ii) it…

Dynamical Systems · Mathematics 2022-05-03 Romeo Ortega , Jose Guadalupe Romero , Stanislav Aranovskiy

In [Han \& Schied, 2023, \textit{arXiv 2307.02582}], an easily computable scale-invariant estimator $\widehat{\mathscr{R}}^s_n$ was constructed to estimate the Hurst parameter of the drifted fractional Brownian motion $X$ from its…

Statistical Finance · Quantitative Finance 2025-09-09 Xiyue Han , Alexander Schied

It is proposed a class of statistical estimators $\hat H =(\hat H_1, \ldots, \hat H_d)$ for the Hurst parameters $H=(H_1, \ldots, H_d)$ of fractional Brownian field via multi-dimensional wavelet analysis and least squares, which are…

Information Theory · Computer Science 2015-02-04 Liang Wu , Yiming Ding

We consider the problem of estimating the roughness of the volatility process in a stochastic volatility model that arises as a nonlinear function of fractional Brownian motion with drift. To this end, we introduce a new estimator that…

Statistical Finance · Quantitative Finance 2026-04-17 Xiyue Han , Alexander Schied

We investigate the problem of estimating the drift parameter from $N$ independent copies of the solution of a stochastic differential equation driven by a multiplicative fractional Brownian noise with Hurst parameter $H\in (1/3,1)$.…

Statistics Theory · Mathematics 2026-05-28 Chiara Amorino , Laure Coutin , Nicolas Marie

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 estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…

Statistics Theory · Mathematics 2014-05-06 Piero Barone , Isabella Lari

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

The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of…

Statistics Theory · Mathematics 2024-11-07 Arnab Ganguly

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…

Statistics Theory · Mathematics 2024-02-16 Carsten Chong , Marc Hoffmann , Yanghui Liu , Mathieu Rosenbaum , Grégoire Szymanski

The paper focuses on the Vasicek model driven by a tempered fractional Brownian motion. We derive the asymptotic distributions of the least-squares estimators (based on continuous-time observations) for the unknown drift parameters. This…

Statistics Theory · Mathematics 2024-06-06 Yuliya Mishura , Kostiantyn Ralchenko , Olena Dehtiar

We study the strong consistency and asymptotic normality of a least squares estimator of the drift coefficient in complex-valued Ornstein-Uhlenbeck processes driven by fractional Brownian motion, extending the results of Chen, Hu, Wang…

Probability · Mathematics 2024-06-27 Fares Alazemi , Abdulaziz Alsenafi , Yong Chen , Hongjuan Zhou

We construct a least squares estimator for the drift parameters of a fractional Ornstein Uhlenbeck process with periodic mean function and long range dependence. For this estimator we prove consistency and asymptotic normality. In contrast…

Statistics Theory · Mathematics 2015-09-11 Herold Dehling , Brice Franke , Jeannette H. C. Woerner

In this paper, we investigate the parameter estimation for threshold Ornstein$\mathit{-}$Uhlenbeck processes. Least squares method is used to obtain continuous-type and discrete-type estimators for the drift parameters based on continuous…

Statistics Theory · Mathematics 2024-03-28 Yuecai Han , Dingwen Zhang

In this article we study the asymptotic behaviour of the least square estimator in a linear regression model based on random observation instances. We provide mild assumptions on the moments and dependence structure on the randomly spaced…

Statistics Theory · Mathematics 2021-10-07 Karine Bertin , Soledad Torres , Lauri Viitasaari

We study efficiency of non-parametric estimation of diffusions (stochastic differential equations driven by Brownian motion) from long stationary trajectories. First, we introduce estimators based on conditional expectation which is…

Probability · Mathematics 2021-05-26 Xi Chen , Ilya Timofeyev