Filtering without recursion and some of its uses in financial economics
Simon Donker van Heel, Neil Shephard
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.
Read the AI summary and key takeaways for traders on WOBR Quant Research.