 Econometric Inference for Regularized Riemann-Liouville Fractional Brownian Motion Second-Order Filtering, HAC-GMM, and Weak IdentificationWorking Papers from HAL Abstract: We develop econometric inference for a regularized Riemann-Liouville fractional Brownian motion observed along one long path. Kernel regularization creates a multiscale variance crossover that identifies the Hurst parameter H and the regularization scale ε, except at the Brownian point H = 1/2, where ε is structurally unidentified. First-order quadratic moments cease to admit a finite root-n long-run variance at H ≥ 3/4. Second-order filtering restores short memory for every H ∈ (0, 1) while preserving the identifying crossover. We establish a functional central limit theorem, consistent HAC covariance estimation, and feasible minimum-distance/HAC-GMM inference. Near H = 1/2, the smallest eigenvalue of the Godambe information matrix is of order (H -1/2) 2 , yielding the mixed rate √ n |H -1/2| for ˆ︁ ε. Monte Carlo evidence documents the filter-order transition, HAC bandwidth sensitivity, and weak-identification distortions predicted by the theory. Keywords: weak identification JEL classification: C13; quadratic variation; identification; C22; Hurst exponent; HAC; Gaussian Volterra process; 62F12; 62M10; 60F17; 60G15; C58 MSC 2020: 60G22; C14; Gaussian Volterra process HAC Hurst exponent identification quadratic variation weak identification JEL classification: C13 (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-05756307 Access Statistics for this paper More papers in Working Papers from HAL |
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