Simon Donker van Heel, Neil Shephard
arXiv 7 Sep 2026 · Econometrics
arXiv:2609.07207 · PDF · Extracted main text
We develop a filter for time series, defined at each time $t$ as the minimizer of a discounted convex combination of observed and expected losses. The filter can be estimated by simulation to an arbitrary level of accuracy in $O(1)$ flops at each time point $t$ and can be run for all values $t=1,...,T$ in parallel. These methods are applied to robustly compute a preaveraged price process from the more than 1.5 million trades made on a single financial asset in a single day where the noise's variance is infinite. It yields a flat "volatility signature" plot, down to the 1 second level, so the microstructure noise no longer biases the volatility estimate. This is not true when linear methods are employed.
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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 | Mykland, P. and L. Zhang (2016) Between data cleaning and inference: Pre-averaging and robust estimators of the efficient price | 0.874 | 11 | 2 | 100% |
| 2 | Jacod, J., Y. Li, P. A. Mykland, M. Podolskij, and M. Vetter (2009) Microstructure noise in the continuous case: The pre-averaging approach | 0.874 | 9 | 2 | 100% |
| 3 | Andersen, T. G., T. Bollerslev, F. X. Diebold, and P. Labys (2001) The distribution of exchange rate volatility | 0.874 | 7 | 2 | 100% |
| 4 | Barndorff-Nielsen, O. E. and N. Shephard (2002) Econometric analysis of realised volatility and its use in estimating stochastic volatility models | 0.874 | 6 | 2 | 100% |
| 5 | Barndorff-Nielsen, O. E., P. R. Hansen, A. Lunde, and N. Shephard (2009) Realised kernels in practice: trades and quotes | 0.644 | 4 | 1 | 100% |
| 6 | Barndorff-Nielsen, O. E., P. R. Hansen, A. Lunde, and N. Shephard (2008) Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise | 0.644 | 2 | 2 | 100% |
| 7 | Corsi, F (2009) A simple long memory model of realized volatility | 0.644 | 2 | 2 | 100% |
| 8 | Koenker, R (2005) Quantile Regression | 0.644 | 2 | 2 | 100% |
| 9 | Zhang, L., P. A. Mykland, and Y. Aẗ-Sahalia (2005) A tale of two time scales: determining integrated volatility with noisy high-frequency data | 0.644 | 2 | 2 | 100% |
| 10 | Donker van Heel, S. and N. Shephard (2025) Exponentially weighted estimands and the exponential family: Filtering, prediction and smoothing | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 82 scored citations.