Inference for SDEs driven by Hermite processes

2025/06/20 by Petr Čoupek, Coupek, Petr, Pavel Kříž +1 · 2 citations
Economics, Econometrics and Finance · Decision Sciences · #Stochastic processes and financial applications #Financial Risk and Volatility Modeling #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.2506.16916

Abstract

In the paper, we address parametric and non-parametric estimation for nonlinear stochastic differential equations with additive Hermite noise with possibly nonlinear scaling. We assume that a single trajectory of the solution is observed discretely and we propose estimators of the Hurst parameter and the Hermite order of the driving process as well as of the average noise intensity and noise intensity function. The estimators are based on the weighted quadratic variation whose properties are used, in particular, to prove weak consistency of the proposed estimators under in-fill asymptotics.

Citations

• Parameter estimation and singularity of laws on the path space for SDEs driven by Rosenblatt processes
• Modified wavelet variation for the Hermite processes
• Asymptotic normality for a modified quadratic variation of the Hermite process
• Wavelet-Type Expansion of Generalized Hermite Processes with rate of convergence
• Multifractional Hermite processes: definition and first properties
• Wavelet methods to study the pointwise regularity of the generalized Rosenblatt process
• Fractal dimensions of the Rosenblatt process
• Stochastic integration with respect to fractional processes in Banach spaces
• Local times and sample path properties of the Rosenblatt process
• A Stochastic Calculus for Rosenblatt Processes
• Lower bound for local oscillations of Hermite processes
• Statistical inference for Vasicek-type model driven by Hermite processes
• A strong convergence to the Rosenblatt process
• Self-similarity parameter estimation and reproduction property for non-Gaussian Hermite processes
• Central and non-central limit theorems for weighted power variations of fractional Brownian motion
• Fractional Brownian Motions, Fractional Noises and Applications

Cited by

• Minimum L₁-norm estimation for fractional Ornstein-Uhlenbeck type process driven by a Hermite process
• On the 1/H-variation of the divergence integral with respect to a Hermite process

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• Stochastic Burgers Equation Driven by a Hermite Sheet with Additive Noise: Existence, Uniqueness, and Regularity
• Nonparametric Estimation in SDE Models Involving an Explanatory Process