Filtering without Recursion and Some of Its Uses in Financial Economics

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.