Parameter estimation of non-ergodic Ornstein-Uhlenbeck

by   Yanping Lu, et al.
Jiangxi Normal University

In this paper, we consider the statistical inference of the drift parameter θ of non-ergodic Ornstein-Uhlenbeck (O-U) process driven by a general Gaussian process (G_t)_t≥ 0. When H ∈ (0, 1/2) ∪ (1/2,1) the second order mixed partial derivative of R (t, s) = E [G_t G_s] can be decomposed into two parts, one of which coincides with that of fractional Brownian motion (fBm), and the other of which is bounded by |ts|^H-1. This condition covers a large number of common Gaussian processes such as fBm, sub-fractional Brownian motion and bi-fractional Brownian motion. Under this condition, we verify that (G_t)_t≥ 0 satisfies the four assumptions in references <cit.>, that is, noise has Hölder continuous path; the variance of noise is bounded by the power function; the asymptotic variance of the solution X_T in the case of ergodic O-U process X exists and strictly positive as T →∞; for fixed s ∈ [0,T), the noise G_s is asymptotically independent of the ergodic solution X_T as T →∞, thus ensure the strong consistency and the asymptotic distribution of the estimator θ̃_T based on continuous observations of X. Verify that (G_t)_t≥ 0 satisfies the assumption in references <cit.>, that is, the variance of the increment process {ζ_t_i-ζ_t_i -1, i =1,..., n } is bounded by the product of a power function and a negative exponential function, which ensure that θ̂_n and θ̌_n are strong consistent and the sequences √(T_n) (θ̂_n - θ) and √(T_n) (θ̌_n - θ) are tight based on discrete observations of X


page 1

page 2

page 3

page 4


Parameter estimation for Vasicek model driven by a general Gaussian noise

This paper developed an inference problem for Vasicek model driven by a ...

Least squares estimation for non-ergodic weighted fractional Ornstein-Uhlenbeck process of general parameters

Let B^a,b:={B_t^a,b,t≥0} be a weighted fractional Brownian motion of par...

Statistical analysis of the non-ergodic fractional Ornstein-Uhlenbeck process with periodic mean

Consider a periodic, mean-reverting Ornstein-Uhlenbeck process X={X_t,t≥...

Estimating drift parameters in a non-ergodic Gaussian Vasicek-type model

We study the problem of parameter estimation for a non-ergodic Gaussian ...

Parameter estimations for the Gaussian process with drift at discrete observation

This paper first strictly proved that the growth of the second moment of...

Estimating the roughness exponent of stochastic volatility from discrete observations of the realized variance

We consider the problem of estimating the roughness of the volatility in...

Please sign up or login with your details

Forgot password? Click here to reset