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Filtering without recursion and some of its uses in financial economics
Abstract
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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BibTeX
@misc{heel2026filtering,
title = {{Filtering without recursion and some of its uses in financial economics}},
author = {Simon Donker van Heel and Neil Shephard},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07207},
eprint = {2609.07207},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07207},
}
RIS
TY - UNPB
TI - Filtering without recursion and some of its uses in financial economics
AU - Simon Donker van Heel
AU - Neil Shephard
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07207
UR - https://arxiv.org/abs/2609.07207
AB - 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.
ER -