Statistical arbitrage, also known as pairs trading, is an important investment strategy in the financial markets. It is usually involved in a serial stages, say, assets selection, model estimation, portfolio design, and mean reversion trading. In this thesis, we will focus on the model estimation and portfolio design parts.

In econometrics and finance, the vector error correction model, or more generally the reduced-rank regression (RRR) model, is an important regression model for cointegration analysis, which is used to estimate the long-run equilibrium variable relationships. In this thesis, we will first study the efficient estimation of sparse RRR models. The traditional analysis and estimation methodologies assume the underlying Gaussian distribution but, in practice, heav...[ Read more ]

Statistical arbitrage, also known as pairs trading, is an important investment strategy in the financial markets. It is usually involved in a serial stages, say, assets selection, model estimation, portfolio design, and mean reversion trading. In this thesis, we will focus on the model estimation and portfolio design parts.

In econometrics and finance, the vector error correction model, or more generally the reduced-rank regression (RRR) model, is an important regression model for cointegration analysis, which is used to estimate the long-run equilibrium variable relationships. In this thesis, we will first study the efficient estimation of sparse RRR models. The traditional analysis and estimation methodologies assume the underlying Gaussian distribution but, in practice, heavy-tailed data and outliers can lead to the inapplicability of these methods. In this thesis, we propose a robust model estimation method based on the Cauchy distribution to deal with the robust estimation of VECM. Efficient algorithms based on the majorization-minimization method is applied to solve these proposed nonconvex problems. The performance of this algorithm is shown through numerical simulations.

The RRR in fact defines a cointegration space for the investment. After finding such a cointegration space, the following step is how to find an investment portfolio within this space. This thesis also considers the mean-reverting portfolio design problem arising from statistical arbitrage. This problem is formulated by optimizing some criteria characterizing the mean-reversion strength of the portfolio and taking into consideration the variance of the portfolio and an investment budget constraint or an investment leverage constraint at the same time. To deal with these problems, efficient algorithms based on nonconvex optimization methods like the majorization-minimization method or the successive convex approximation method are proposed. Numerical results show that our proposed mean-reverting portfolio design methods can show superior performance in the markets.