Parameter estimation for fractional Ornstein–Uhlenbeck processes

By Yaozhong Hu, David Nualart. 2009

331 citations recorded by the source corpus.

We study a least squares estimator for the Ornstein-Uhlenbeck process, , driven by fractional Brownian motion BH with Hurst parameter . We prove the strong consistence of (the almost surely convergence of to the true parameter [theta]). We also obtain the rate of this convergence when 1/2

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f2e6a8b491a50d2958ee4dd205ab4882d8700df1

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Citations in the corpus

Least squares estimator for non-ergodic Ornstein-Uhlenbeck processes driven by Gaussian processes (2015, methodology): “Moreover, as an application, the models discussed in [10], [1], [2], [6] have been studied in [9] by using this approach.”
A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise (2011, methodology): “in Belfadli et al. (2011), Hu and Nualart (2010), Kleptsyna and Le Breton (2002), Le Breton (1998), Papavasiliou and Ladroue (2011), Prakasa Rao (2010), Tudor and Viens (2007). Estimators based on discrete time data, which are important for practical applications, are then obtained via discretizatio”
Optimal rates for parameter estimation of stationary Gaussian processes (2016, methodology): “It should be noted that in [14], the full LS estimator relies on an unobservable Skorohod integral, and the authors proposed a modified version of this estimator which can be computed based on in-fill asymptotics; however, this modified estimator bears no immediate relation to an LS one (see [13] fo”
Statistical inference for Vasicek-type model driven by Hermite processes (2017, background): “(2.16) Identity (2.16) comes from (2H − 1) ∫ [0,∞)2 e−a(t+s)|t− s|2H−2dsdt = a−2H(2H − 1) ∫ [0,∞)2 e−(t+s)|t− s|2H−2dsdt = a−2HΓ(2H), (2.17) see, e.g., Lemma 5.1 in Hu-Nualart [12] for the second equality.”
Parameter Estimation for Fractional Ornstein-Uhlenbeck Processes: Non-ergodic Case (2011, methodology): “In the case θ 0 (corresponding to the ergodic case), Hu and Nualart [7] studied the parameter estimation for θ by using the least squares estimator (LSE) defined as θ̂t = ∫ t 0 XsdXs∫ t 0 X2sds , t ≥ 0.”
ASYMPTOTIC THEORY FOR ESTIMATING DRIFT PARAMETERS IN THE FRACTIONAL VASICEK MODEL (2018, methodology): “1 extends that of Hu and Nualart (2010) from the fOU model to the fVm. Remark 3.2. Applying the well-known result 1 T ∫ T 0 ∫ t 0 s 2H−2e−κsdsdt → κ1−2H (2H − 1) to (3.2) and (3.3) and using Lemma 5.2 in Hu and Nualart (2010), we can show that κ̂L S a.”
On drift parameter estimation in models with fractional Brownian motion (2011, methodology): “Similar approach was applied in [2] to the fractional Ornstein–Uhlenbeck process with constant coefficients.”
Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter (2017, methodology): “In the above lemma, we do not give a statement when H ∈ [(1) 2 , 3 4), because this case has been studied in [11].”
Parameter estimation for a partially observed Ornstein–Uhlenbeck process with long-memory noise (2015, methodology): “4 X and V are observed When both X and V are observed, the estimator of θ∗ based on continuous data is θ̂T given in (9) but the estimator of ρ becomes the usual full-observation estimator of an fBm-driven Ornstein-Uhlenbeck process as in [14], i.”
Exact maximum likelihood estimators for drift fractional Brownian motions (2009, methodology): “But we shall use the method of [6] which seems to be the simplest one to us.”