AI 中文总结
本文提出一种无递归的时间序列滤波方法，通过模拟实现高效并行计算，并应用于高频金融数据，有效消除微观结构噪声对波动率估计的偏差。
AI 中文摘要
我们开发了一种时间序列滤波器，在每一时刻 $t$ 定义为观测损失与期望损失的折现凸组合的最小化器。该滤波器可通过模拟以任意精度估计，在每一时刻 $t$ 仅需 $O(1)$ 次浮点运算，且所有 $t=1,...,T$ 的值可并行计算。我们将这些方法应用于稳健地计算预平均价格过程，数据来自单一金融资产在单日内超过150万笔交易，且噪声方差为无穷大。该方法在低至1秒的时间尺度上产生平坦的“波动率特征”图，因此微观结构噪声不再使波动率估计产生偏差。而使用线性方法时则无法实现这一点。
英文摘要
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.
