Statistical aspects of the fractional stochastic calculus

By Ciprian A. Tudor, Frederi G. Viens. 2006

172 citations recorded by the source corpus.

We apply the techniques of stochastic integration with respect to the fractional Brownian motion and the Gaussian theory of regularity and supremum estimation to study the maximum likelihood estimator (MLE) for the drift parameter of stochastic processes satisfying stochastic equations driven by fractional Brownian motion with any level of H\"{o}lder-regularity (any \emph{Hurst} parameter). We prove existence and strong consistency of the MLE for linear and nonlinear equations. We\ also prove that a basic discretized version of the MLE, is still a strongly consistent estimator.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/232ab27f1cc9f542c60afe5f864e305c78a29a04

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Citations in the corpus

Optimal rates for parameter estimation of stationary Gaussian processes (2016, background): “The work in [27] is the only one in which a strongly consistent discretization of the MLE was based on long-horizon asymptotics without also requiring an in-fill (small time step) condition, though it did not establish any asymptotic distribution.”
Parameter estimation for a partially observed Ornstein–Uhlenbeck process with long-memory noise (2015, background): “A handful of authors are beginning to look at these questions with various fBm-driven models, starting with [28] in 2007, and more recently [3, 7, 11, 20].”
Statistical inference for Vasicek-type model driven by Hermite processes (2017, unknown): “[15] M. Maejima, C. A. Tudor (2007): Wiener integrals with respect to the Hermite process and a non-central limit theorem.”
Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter (2017, background): “It is worth noting that Tudor and Viens have also obtained the almost sure convergence of both the MLE and a version of the MLE using discrete observations for all H ∈ (0, 1) (see Tudor and Viens 2007).”
A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise (2011, result): “(iii) Our current work probably compares best with the maximum likelihood estimator analyzed in [22].”
Least squares estimator for non-ergodic Ornstein-Uhlenbeck processes driven by Gaussian processes (2015, methodology): “We will recall several approaches to estimate the parameters in fractional models but we mention that the list below is not exhaustive: - The MLE approach in [12], [16]: In general the techniques used to construct maximum likelihood estimators (MLE) for the drift parameter are based on Girsanov’s tr”