Flexible least squares for temporal data mining and statistical arbitrage

Abstract

A number of recent emerging applications call for studying data streams, potentially infinite flows of information updated in realtime. 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.

Dynamically Mixing Dynamic Linear Models With Applications in Finance

“…In section §4, we introduce an alternative set of widely available financial time series permitting easier replication of the work in (Montana et al, 2009); and we provide an example of applying a mixture model to real world financial data, extracting insightful time varying estimates of variance in an ETF returns model during the recent financial crisis. In section §5, we augment the statistical arbitrage strategy proposed in (Montana et al, 2009) by incorporating a hedge that significantly improves strategy performance. We demonstrate that an on-line dynamic mixture model outperforms all statically parameterized DLMs.…”

“…The increased observational variance at the end of 2008, visible in Figure 6 results in an increase in the rate of profitability of the statistical arbitrage application plainly visible in Figure 7. (Montana et al, 2009) describe an illustrative statistical arbitrage strategy. Their proposed strategy takes equal value trading positions opposite the sign of the most recently observed forecast error ε t−1 .…”

“…4 A FINANCIAL EXAMPLE (Montana et al, 2009) proposed a model for the returns of the S&P 500 Index based upon the largest principal component of the underlying stock returns. In the form Y = F T θ + ε used throughout this paper, Y = r s&p , F = r pc1 , and θ = β pc1 .…”

“…The target and explanatory data in (Montana et al, 2009) spanned January 1997 to October 2005. We propose the use of two alternative price series that are very similar in nature; but, publicly available, widely disseminated, and tradeable.…”

Rate Parameter Distributions for Isobutane Dehydrogenation and Isobutene Dimerization and Desorption over HZSM-5

“…As μ approaches infinity the parameter determination approach the zero dynamic cost (ordinary least squares) solution [3,33]. When μ is set close to zero, priority is given to the dynamic specification and to estimates of the time-varying parameters [34], and hence a closer fit to the data (μ = 0.001 was used). For temperature-programmed rate data log 56 (27) …”