Flexible Least Squares for Dynamic Statistical Arbitrage

Summary

This paper considers how to model changing relationships among multiple data streams that evolve over time. It focuses on flexible least squares (FLS), which modifies ordinary least squares with a penalty that allows regression coefficients to vary, without requiring a restrictive probability model for those dependencies. Statistical arbitrage is the motivating financial application.

The authors show an algebraic equivalence between FLS and Kalman filter equations, using that connection to clarify the method and propose a more efficient algorithm. They report promising experiments from an algorithmic trading system applied to the S&P 500 Futures Index. The supplied description does not specify the trading rules, evaluation period, costs, benchmark, or numerical performance, so it offers limited evidence for practical profitability. Its main contribution, as described, is the dynamic estimation approach and its computational connection to filtering methods.

Key ideas

• FLS estimates relationships between evolving data streams while allowing regression coefficients to change over time.
• Its penalized least-squares formulation avoids imposing a restrictive probabilistic law on changing dependencies.
• The paper establishes an algebraic equivalence between FLS and Kalman filter equations.
• That equivalence is used to explain the method and motivate a more efficient algorithm.
• Experiments on an S&P 500 futures index trading system are described as promising, but detailed performance evidence is absent.

Tags

# Flexible least squares for temporal data mining and statistical arbitrage


# Flexible least squares for temporal data mining and statistical arbitrage









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.

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