Mikkel Bennedsen, Kim Christensen, Peter Korsbakke Christensen, Jun Yu, Chen Zhang
arXiv 18 Sep 2026 · Econometrics
arXiv:2609.21587 · PDF · Extracted main text
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 coefficient 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 coefficients 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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Corsi (2009) A simple approximate long-memory model of realized volatility | 1.000 | 7 | 3 | 100% |
| 2 | Gatheral, Jaisson, and Rosenbaum (2018) Volatility is rough | 1.000 | 6 | 4 | 100% |
| 3 | Bennedsen, Christensen, and Christensen (2026) To be or not to be: Roughness or long memory in volatility? self | 0.874 | 6 | 2 | 100% |
| 4 | Wang, Xiao, and Yu (2023) Modeling and forecasting realized volatility with the fractional Ornstein-Uhlenbeck process self | 0.874 | 6 | 2 | 100% |
| 5 | Bollerslev, Patton, and Quaedvlieg (2016) Exploiting the errors: A simple approach for improved volatility forecasting | 0.874 | 5 | 2 | 100% |
| 6 | Shi, Yu, and Zhang (2024) On the spectral density of fractional Ornstein-Uhlenbeck processes self | 0.843 | 3 | 3 | 100% |
| 7 | Wang, Xiao, Yu, and Zhang (2025) Maximum likelihood estimation of fractional Ornstein-Uhlenbeck process with discretely sampled data | 0.843 | 3 | 3 | 100% |
| 8 | Barndorff-Nielsen and Shephard (2002) Econometric analysis of realized volatility and its use in estimating stochastic volatility models | 0.737 | 3 | 2 | 100% |
| 9 | Bibinger, Yu, and Zhang (2025) Modeling and forecasting realized volatility with multivariate fractional Brownian motion self | 0.737 | 3 | 2 | 100% |
| 10 | Bolko, Christensen, Pakkanen, and Veliyev (2023) A GMM approach to estimate the roughness of stochastic volatility | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 57 scored citations.