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.Comment: 34 pages, 6 figures. Submitte

Obtaining initial parameter estimates for chaotic dynamical systems using linear associative memories

Parameter estimation problems for nonlinear dynamical sg stems are typically formulated as nonlinear optimization problems. For such problems, one has the usual difficulty that standard successive approximation schemes generally require good initial parameter estimates in order to converge to the truth. The linear associative memory method has demonstrated its effectiveness in obtaining useful initial parameter estimates for simple nonlinear dynamical systems. No work, however, has yet been done to apply this method to a chaotic system. This paper initiates' such a study using the logistic map, which is capable of generating mathematical chaos. Supervised training was conducted between system parameters and system outputs to construct optimal memory matrices. Untrained system outputs were then used together with the memory matrices to estimate system parameters. Very accurate parameter estimates were obtained for noise-free system outputs. Good parameter estimates were obtained for system outputs corrupted by noise. A `'rule of thumb'' is suggested that can be used to aid in a successful search for true parameter values if the initial training range is not located `'near'' them

Bootstrap Inference of Level Relationships in the Presence of Serially Correlated Errors: A Large Scale Simulation Study and an Application in Energy Demand

By undertaking a large scale simulation study, we demonstrate that the maximum entropy bootstrap (meboot) data generation process can provide accurate and narrow parameter confidence intervals in models with combinations of stationary and nonstationary variables, under both low and high degrees of autocorrelation. The relatively small sample sizes in which meboot performs particularly well make it a useful tool for rolling window estimation. As a case study, we analyze the evolution of the price and income elasticities of import demand for crude oil in Turkey by using quarterly data between 1996-2011. Our approach can be employed to tackle a wide range of macroeconometric estimation problems where small sample sizes are a common issue