Kalman Filters
Optimally estimating the state of a system from a series of incomplete and noisy measurements.
Finding the Signal in the Noise
A Kalman filter is a powerful algorithm that can estimate the internal state of a system when you can't observe it directly. It works by making a prediction, taking a noisy measurement, and then smartly combining the two to produce an optimal estimate.
In quantitative finance, it's used in pairs trading to estimate the "true" underlying spread between two assets, for dynamic hedging, and for creating smooth estimates of noisy indicators. It excels at finding the hidden "signal" within a stream of chaotic market data.
Interactive Kalman Filter
Adjust the noise parameters to see how the Kalman filter performs. A high measurement noise means your observations are unreliable, forcing the filter to trust its own predictions more.