scholarly journals Asymptotic properties for the parameter estimation in Ornstein-Uhlenbeck process with discrete observations

2020 ◽  
Vol 14 (2) ◽  
pp. 3192-3229
Author(s):  
Hui Jiang ◽  
Hui Liu ◽  
Youzhou Zhou
Keyword(s):  
Parameter Estimation ◽  
Asymptotic Properties ◽  
Discrete Observations ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process

Parameter estimation for a partially observed Ornstein–Uhlenbeck process with long-memory noise

Stochastics ◽  
2016 ◽  
Vol 89 (2) ◽  
pp. 431-468 ◽  
Author(s):  
Brahim El Onsy ◽  
Khalifa Es-Sebaiy ◽  
Frederi G. Viens
Keyword(s):  
Parameter Estimation ◽  
Long Memory ◽  
Uhlenbeck Process ◽  
Partially Observed ◽  
Ornstein Uhlenbeck Process

scholarly journals Berry–Esséen bound for the parameter estimation of fractional Ornstein–Uhlenbeck processes

2019 ◽  
Vol 20 (04) ◽  
pp. 2050023 ◽  
Author(s):  
Yong Chen ◽  
Nenghui Kuang ◽  
Ying Li
Keyword(s):  
Parameter Estimation ◽  
Brownian Motion ◽  
Continuous Time ◽  
Index Formula ◽  
Hurst Index ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Time Observation ◽  
Statistical Estimations ◽  
Drift Parameter

For an Ornstein–Uhlenbeck process driven by fractional Brownian motion with Hurst index [Formula: see text], we show the Berry–Esséen bound of the least squares estimator of the drift parameter based on the continuous-time observation. We use an approach based on Malliavin calculus given by Kim and Park [Optimal Berry–Esséen bound for statistical estimations and its application to SPDE, J. Multivariate Anal. 155 (2017) 284–304].

Modeling Copper Prices: Ornstein-Uhlenbeck Process and Jump-Diffusions

2012 ◽  
Vol 461 ◽  
pp. 793-796
Author(s):  
Xi Bing Li ◽  
Yu Xi Hu ◽  
Zhen Zhong Zhang ◽  
Xin Ru Liu
Keyword(s):  
Parameter Estimation ◽  
Moment Method ◽  
Futures Market ◽  
Uhlenbeck Process ◽  
Jump Diffusions ◽  
Ornstein Uhlenbeck Process ◽  
Futures Price ◽  
Generalized Moment

In this paper we focus on parameter estimation of the futures price processes with a Ornstein-Uhlenbeck process and jump-diffusions. We use the generalized moment method to derive the OU process. Afterwards, we fit a jump diffusions model to Copper prices from Shanghai Copper futures market.

Self-normalized asymptotic properties for the parameter estimation in fractional Ornstein–Uhlenbeck process

2019 ◽  
Vol 19 (03) ◽  
pp. 1950018 ◽  
Author(s):  
Hui Jiang ◽  
Junfeng Liu ◽  
Shaochen Wang
Keyword(s):  
Large Deviations ◽  
Asymptotic Properties ◽  
Moderate Deviations ◽  
Delta Method ◽  
Fourth Moment ◽  
Test Statistics ◽  
Uhlenbeck Process ◽  
Ornstein Uhlenbeck Process ◽  
Deviation Inequalities ◽  
Type Ii Errors

In this paper, we consider the self-normalized asymptotic properties of the parameter estimators in the fractional Ornstein–Uhlenbeck process. The deviation inequalities, Cramér-type moderate deviations and Berry–Esseen bounds are obtained. The main methods include the deviation inequalities and moderate deviations for multiple Wiener–Itô integrals [P. Major, Tail behavior of multiple integrals and U-statistics, Probab. Surv. 2 (2005) 448–505; On a multivariate version of Bernsteins inequality, Electron. J. Probab. 12 (2007) 966–988; M. Schulte and C. Thäle, Cumulants on Wiener chaos: Moderate deviations and the fourth moment theorem, J. Funct. Anal. 270 (2016) 2223–2248], as well as the Delta methods in large deviations [F. Q. Gao and X. Q. Zhao, Delta method in large deviations and moderate deviations for estimators, Ann. Statist. 39 (2011) 1211–1240]. For applications, we propose two test statistics which can be used to construct confidence intervals and rejection regions in the hypothesis testing for the drift coefficient. It is shown that the Type II errors tend to be zero exponential when using the proposed test statistics.

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