Matrix Cointegration for Structured Time Series and Pairs Trading

Summary

The document introduces a cointegrated autoregressive model for time series whose observations are matrices. Its cointegrating relationships are bilinear, representing structure across both rows and columns. This formulation is intended to retain matrix organization and support interpretations that ordinary cointegration may not capture as directly. The authors describe least-squares and maximum-likelihood estimators for the cointegrating vectors and other model parameters, and derive asymptotic distributions when trends are present.

The evidence described includes simulations comparing the method with traditional approaches and an application to Fama-French portfolios, from which the authors develop a pairs-trading strategy. The summary claims stronger simulation performance but provides no details about the data setup, metrics, or trading results. It also does not specify implementation choices such as signal construction, transaction costs, or risk controls. Thus, the document presents a statistical modeling framework and an illustrative trading application, rather than enough information to assess whether the strategy would perform after costs or generalize to other portfolios.

Key ideas

• The model represents cointegration in matrix-valued data through bilinear row and column relationships.
• Least-squares and maximum-likelihood methods estimate the cointegrating vectors and remaining model parameters.
• The authors establish asymptotic results for trending matrix autoregressions.
• Simulations and a Fama-French portfolio application illustrate the method, including a pairs-trading strategy.

Tags

# Cointegrated Matrix Autoregression Models


# Cointegrated Matrix Autoregression Models









We propose a novel cointegrated autoregressive model for matrix-valued time series, with bi-linear cointegrating vectors corresponding to the rows and columns of the matrix data. Compared to the traditional cointegration analysis, our proposed matrix cointegration model better preserves the inherent structure of the data and enables corresponding interpretations. To estimate the cointegrating vectors as well as other coefficients, we introduce two types of estimators based on least squares and maximum likelihood. We investigate the asymptotic properties of the cointegrated matrix autoregressive model under the existence of trend and establish the asymptotic distributions for the cointegrating vectors, as well as other model parameters. We conduct extensive simulations to demonstrate its superior performance over traditional methods. In addition, we apply our proposed model to Fama-French portfolios and develop a effective pairs trading strategy.

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