Mean Reversion with a Variance Threshold

Marco Cuturi (1) , Alexandre d'Aspremont (2, 3)

1 Department of Social Informatics [Kyoto]
2 LIENS - Laboratoire d'informatique de l'école normale supérieure
3 SIERRA - Statistical Machine Learning and Parsimony

Starting from a multivariate data set, we study several techniques to isolate affine combinations of the variables with a maximum amount of mean reversion, while constraining the variance to be larger than a given threshold. We show that many of the optimization problems arising in this context can be solved exactly using semidefinite programming and some variant of the S-lemma. In finance, these methods are used to isolate statistical arbitrage opportunities, i.e. mean reverting portfolios with enough variance to overcome market friction. In a more general setting, mean reversion and its generalizations are also used as a proxy for stationarity, while variance simply measures signal strength.

Domaines: Recherche opérationnelle [math.OC]

Marco Cuturi, Alexandre d'Aspremont. Mean Reversion with a Variance Threshold. International Conference on Machine Learning, Jun 2013, United States. pp.271-279. ⟨hal-00939566⟩