Multi-Power Inference Beyond Semimartingales: Rough Gaussian Activity and Jumps

Jules Sadefo Kamdem

Working Papers from HAL

Abstract: We study multiscale inference based on realized power variations when the continuous component of an observed process is rougher than a Brownian semimartingale. The continuous component is locally Gaussian with scaling exponent H < 1/2, and the model may additionally contain discontinuous activity. Realized p-variation then scales as ∆ pH-1 n , generating distinct regimes according to whether pH is below, at, or above one. At the critical boundary pH = 1, a continuous rough process may share the same first-order two-scale activity signature as a process containing jumps, creating an identification problem outside the usual semimartingale framework. We develop joint inference across several powers rather than relying on a single activity statistic. For the fractional Brownian benchmark, we derive a joint central limit theorem for the multi-power signatures and a roughness estimator computed from the same sample. This leads to a feasible quadratic specification statistic Q n whose null limit is chi-square. Under n -1/2 -local departures from the rough scaling relation, Q n has a noncentral chi-square limit, yielding an explicit asymptotic power function, while fixed identifiable alternatives are detected consistently. Gaussian Volterra extensions are obtained under explicit local-scaling and correlation-summability conditions. Monte Carlo experiments document the finite-sample size-power trade-off associated with using high powers and examine robustness to infinite-activity jumps, microstructure noise, and irregular sampling.

Keywords: multi-power inference; rough Gaussian processes; Gaussian Volterra processes; fractional Brownian motion; power variation; specification testing; jump activity; high-frequency econometrics (search for similar items in EconPapers)
Date: 2026-09-21
Note: View the original document on HAL open archive server: https://hal.science/hal-05756501v1
References: Add references at CitEc
Citations:

Downloads: (external link)
https://hal.science/hal-05756501v1/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-05756501

Access Statistics for this paper

More papers in Working Papers from HAL
Bibliographic data for series maintained by CCSD ().