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We construct an objective function that consists of a quadratic approximation term and a penalty term. Thanks to the quadratic approximation, we can deal with various kinds of loss functions into a unified way, and by taking advantage of…

Statistics Theory · Mathematics 2018-11-26 Takumi Suzuki , Nakahiro Yoshida

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

Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…

Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a…

Statistics Theory · Mathematics 2014-01-30 Minjing Tao , Yazhen Wang , Harrison H. Zhou

We study the joint asymptotic distribution of the least squares estimator of the parameter $(\theta,\,\mu)$ for the non-ergodic Vasicek models driven by seven specific Gaussian processes. %The similar result concerning to the non-ergodic…

Probability · Mathematics 2024-12-03 Yong Chen , Wu-Jun Gao , Ying Li

We study the problem of parameter estimation for discretely observed stochastic differential equations driven by small fractional noise. Under some conditions, we obtain strong consistency and rate of convergence of the least square…

Statistics Theory · Mathematics 2022-01-24 S. Nakajima , S. Nakamura , Y. Shimizu

The purpose of this paper is to study the asymptotic behavior of the weighted least square estimators of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on the immigration and…

Probability · Mathematics 2015-03-20 Vassili Blandin

Misspecified models often provide useful information about the true data generating distribution. For example, if $y$ is a non-linear function of $x$ the least squares estimator $\hat{\beta}$ is an estimate of $\beta$, the slope of the best…

Methodology · Statistics 2017-05-17 James P. Long

In this paper, we study finite-sample properties of the least squares estimator in first order autoregressive processes. By leveraging a result from decoupling theory, we derive upper bounds on the probability that the estimate deviates by…

Statistics Theory · Mathematics 2020-05-26 Rodrigo A. González , Cristian R. Rojas

This article studies the finite sample behaviour of a number of estimators for the integrated power volatility process of a Brownian semistationary process in the non semi-martingale setting. We establish three consistent feasible…

Statistics Theory · Mathematics 2021-06-18 Phillip Murray , Riccardo Passeggeri , Almut E. D. Veraart , Mikko S. Pakkanen

We provide an efficient and accurate simulation scheme for the rough Heston model in the standard ($H>0$) as well as the hyper-rough regime ($H > -1/2$). The scheme is based on low-dimensional Markovian approximations of the rough Heston…

Computational Finance · Quantitative Finance 2023-10-09 Christian Bayer , Simon Breneis

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

We study a least square-type estimator for an unknown parameter in the drift coefficient of a stochastic differential equation with additive fractional noise of Hurst parameter H>1/2. The estimator is based on discrete time observations of…

Probability · Mathematics 2011-11-10 Andreas Neuenkirch , Samy Tindel

Error-in-variables regression is a common ingredient in treatment effect estimators using panel data. This includes synthetic control estimators, counterfactual time series forecasting estimators, and combinations. We study high-dimensional…

Statistics Theory · Mathematics 2021-04-20 David A. Hirshberg

In this paper we estimate both the Hurst and the stable indices of a H-self-similar stable process. More precisely, let $X$ be a $H$-sssi (self-similar stationary increments) symmetric $\alpha$-stable process. The process $X$ is observed at…

Statistics Theory · Mathematics 2017-10-19 Thi To Nhu Dang , Jacques Istas

We consider the parameter estimation problem for the non-ergodic fractional Ornstein-Uhlenbeck process defined as $dX_t=\theta X_tdt+dB_t,\ t\geq0$, with a parameter $\theta>0$, where $B$ is a fractional Brownian motion of Hurst index…

Probability · Mathematics 2011-03-01 Rachid Belfadli , Khalifa Es-Sebaiy , Youssef Ouknine

In this paper, we construct consistent statistical estimators of the Hurst index, volatility coefficient, and drift parameter for Bessel processes driven by fractional Brownian motion with $H<1/2$. As an auxiliary result, we also prove the…

Probability · Mathematics 2023-05-25 Yuliya Mishura , Anton Yurchenko-Tytarenko

A one dimensional diffusion process $X=\{X_t, 0\leq t \leq T\}$, with drift $b(x)$ and diffusion coefficient $\sigma(\theta, x)=\sqrt{\theta} \sigma(x)$ known up to $\theta>0$, is supposed to switch volatility regime at some point $t^*\in…

Statistics Theory · Mathematics 2007-09-20 A. De Gregorio , S. M. Iacus

We solve the first-passage problem for the Heston random diffusion model. We obtain exact analytical expressions for the survival and hitting probabilities to a given level of return. We study several asymptotic behaviors and obtain…

Statistical Finance · Quantitative Finance 2010-03-25 Jaume Masoliver , Josep Perello

The partially observed linear Gaussian system of stochastic differential equations with low noise in observations is considered. A kernel-type estimators are used for estimation of the quadratic variation of the derivative of the limit of…

Statistics Theory · Mathematics 2022-11-23 Yury A. Kutoyants