arXiv subjects

Kohei Chiba

Publications and source records attributed to Kohei Chiba.

3 recordsLinked to original sources

arXiv2022

Asymptotically Efficient Estimation of Ergodic Rough Fractional Ornstein-Uhlenbeck Process under Continuous Observations

We consider the problem of asymptotically efficient estimation of drift parameters of the ergodic fractional Ornstein-Uhlenbeck process under continuous observations when the Hurst parameter $H<1/2$ and the mean of its stationary distribution is not equal to zero. In this paper, we derive asymptotically efficient rates and variances of estimators of drift parameters and prove an asymptotic efficiency of a maximum likelihood estimator of drift parameters.

math.ST↗

arXiv2018

LAN property for stochastic differential equations driven by fractional Brownian motion of Hurst parameter $H\in(1/4,1/2)$

In this paper, we consider the problem of estimating the drift parameter of solution to the stochastic differential equation driven by a fractional Brownian motion with Hurst parameter less than $1/2$ under complete observation. We derive a formula for the likelihood ratio and prove local asymptotic normality when $H \in (1/4,1/2)$. Our result shows that the convergence rate is $T^{-1/2}$ for the parameters satisfying a certain equation and $T^{-(1-H)}$ for the others.

math.ST↗

arXiv2018

Estimation of the lead-lag parameter between two stochastic processes driven by fractional Brownian motions

In this paper, we consider the problem of estimating the lead-lag parameter between two stochastic processes driven by fractional Brownian motions (fBMs) of the Hurst parameter greater than 1/2. First we propose a lead-lag model between two stochastic processes involving fBMs, and then construct a consistent estimator of the lead-lag parameter with possible convergence rate. Our estimator has the following two features. Firstly, we can construct the lead-lag estimator without using the Hurst parameters of the underlying fBMs. Secondly, our estimator can deal with some non-synchronous and irregular observations. We explicitly calculate possible convergence rate when the observation times are (1) synchronous and equidistant, and (2) given by the Poisson sampling scheme. We also present numerical simulations of our results using the R package YUIMA.

math.ST↗