Nonparametric estimation of the local Hurst function of multifractional Gaussian processes

Abstract

A new nonparametric estimator of the local Hurst function of a multifractional Gaussian process based on the increment ratio (IR) statistic is defined. In a general frame, the point-wise and uniform weak and strong consistency and a multidimensional central limit theorem for this estimator are established. Similar results are obtained for a refinement of the generalized quadratic variations (QV) estimator. The example of the multifractional Brownian motion is studied in detail. A simulation study is included showing that the IR-estimator is more accurate than the QV-estimator.

References in corpus (2)

• Nonparametric estimation of the local Hurst function of multifractional Gaussian processes
• Asymptotic expansion and central limit theorem for quadratic variations of Gaussian processes

Cited by in corpus (7)

• Nonparametric estimation of the local Hurst function of multifractional Gaussian processes
• Regularity of multifractional moving average processes with random Hurst exponent
• A General Class of Multifractional Processes and Stock Price Informativeness
• Exact uniform modulus of continuity and Chung's LIL for the generalized fractional Brownian motion
• Linear Multifractional Stable Motion: wavelet estimation of $H(\cdot )$ and $\al$ parameters
• Estimation of the Pointwise Hölder Exponent of Hidden Multifractional Brownian Motion Using Wavelet Coefficients
• Uniformly and strongly consistent estimation for the Hurst function of a Linear Multifractional Stable Motion