Filtering without recursion and some of its uses in financial economics

2026-09-07

AI Summary

本文提出了一种非递归滤波器，通过最小化折现的凸组合损失来处理时间序列，并应用于金融资产交易数据中以消除微观结构噪声对波动率估计的影响。

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.

Problem

• time series
• filtering
• financial economics
• microstructure noise
• volatility estimation

Innovation

• filter
• time series
• discounted convex combination
• parallel processing
• microstructure noise