  A number of recent emerging applications call for studying data streams,
potentially infinite flows of information updated in real-time. When multiple
co-evolving data streams are observed, an important task is to determine how
these streams depend on each other, accounting for dynamic dependence patterns
without imposing any restrictive probabilistic law governing this dependence.
In this paper we argue that flexible least squares (FLS), a penalized version
of ordinary least squares that accommodates for time-varying regression
coefficients, can be deployed successfully in this context. Our motivating
application is statistical arbitrage, an investment strategy that exploits
patterns detected in financial data streams. We demonstrate that FLS is
algebraically equivalent to the well-known Kalman filter equations, and take
advantage of this equivalence to gain a better understanding of FLS and suggest
a more efficient algorithm. Promising experimental results obtained from a
FLS-based algorithmic trading system for the S&P 500 Futures Index are
reported.
