Online State-Space Estimation of Mean-Reverting Spreads for Statistical Arbitrage

Summary

This paper develops a state-space approach to modeling mean-reverting spreads used in statistical arbitrage, including pairs trading. It treats observed spreads as noisy readings of hidden states and uses real-time estimates of those states to identify temporary market inefficiencies. The framework extends earlier Gaussian linear state-space models by allowing parameters to change over time, helping the estimates adapt as the data-generating process shifts.

The authors also introduce an online estimation algorithm intended to run continuously, including with high-frequency data, and produce uncertainty measures for estimated parameters. They discuss experiments using Monte Carlo simulations and historical equity data, including a cointegration relationship between two exchange-traded funds. The document gives no performance figures or trading-cost analysis, so it does not establish that detected inefficiencies translate into executable excess returns. Its evidence is described at a high level, without enough detail here to assess robustness.

Key ideas

• The framework models observed spreads as noisy realizations of hidden states in a Gaussian linear state-space process.
• Allowing model parameters to vary over time supports adaptation to changing data.
• An online algorithm estimates the latent spread and parameters in real time.
• Parameter uncertainty measures can inform monitoring of mean reversion.
• Monte Carlo and historical equity examples are described, including a cointegration relationship between two ETFs.

Tags

# Dynamic modeling of mean-reverting spreads for statistical arbitrage


# Dynamic modeling of mean-reverting spreads for statistical arbitrage









Statistical arbitrage strategies, such as pairs trading and its generalizations, rely on the construction of mean-reverting spreads enjoying a certain degree of predictability. Gaussian linear state-space processes have recently been proposed as a model for such spreads under the assumption that the observed process is a noisy realization of some hidden states. Real-time estimation of the unobserved spread process can reveal temporary market inefficiencies which can then be exploited to generate excess returns. Building on previous work, we embrace the state-space framework for modeling spread processes and extend this methodology along three different directions. First, we introduce time-dependency in the model parameters, which allows for quick adaptation to changes in the data generating process. Second, we provide an on-line estimation algorithm that can be constantly run in real-time. Being computationally fast, the algorithm is particularly suitable for building aggressive trading strategies based on high-frequency data and may be used as a monitoring device for mean-reversion. Finally, our framework naturally provides informative uncertainty measures of all the estimated parameters. Experimental results based on Monte Carlo simulations and historical equity data are discussed, including a co-integration relationship involving two exchange-traded funds.

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