The "Rough" HAR model

Mikkel Bennedsen, Kim Christensen, Peter Korsbakke Christensen, Jun Yu and Chen Zhang
Additional contact information
Mikkel Bennedsen: Aarhus University, Department of Economics and Business Economics, Denmark
Kim Christensen: Aarhus University, Department of Economics and Business Economics, Denmark
Peter Korsbakke Christensen: Aarhus University, Department of Economics and Business Economics, Denmark
Jun Yu: University of Macau, Faculty of Business Administration, Macau
Chen Zhang: Sun Yat-sen University, Lingnan College, China

No 202646, Working Papers from University of Macau, Faculty of Business Administration

Abstract: This paper proposes discrete-time approximations to rough continuous-time models of realized variance (RV). The leading rough models can be viewed as autoregressive processes driven by fractional Gaussian noise. We show that the Wold representation of this noise concentrates its dependence at the first lag when the Hurst parameter is below one half. Augmenting the autoregressive (AR) and heterogeneous autoregressive (HAR) models with a first-order moving-average (MA(1)) component therefore approximates the roughness, and the MA coeffcient maps almost linearly into the Hurst parameter. We refer to these extensions as the "rough" AR and "rough" HAR models. Estimating them on the log RV of ten ETFs, we find negative MA coeffcients for every asset, and the implied Hurst parameters align closely with the estimates from the continuous-time models. In the HAR literature, the negative MA(1) component is a significant feature that has been largely overlooked. In out-of-sample comparisons, the "rough"" models outperform their classical counterparts for nearly every asset and horizon, with the largest gains at short horizons, and their accuracy is comparable to that of the rough continuous-time models but much easier to estimate by standard off-the-shelf software.

Keywords: Continuous-time models; roughness; HAR model; realized variance (search for similar items in EconPapers)
JEL-codes: C10 C58 C80 (search for similar items in EconPapers)
Pages: 42 pages
Date: 2026-09
References: Add references at CitEc
Citations:

Published in UM-FBA Working Paper Series

Downloads: (external link)
https://fba.um.edu.mo/wp-content/uploads/RePEc/doc/202646.pdf (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:boa:wpaper:202646

Access Statistics for this paper

More papers in Working Papers from University of Macau, Faculty of Business Administration Contact information at EDIRC.
Bibliographic data for series maintained by Carla Leong ().