Mean Reversion with a Variance Threshold.

  • TITLE: Mean Reversion with a Variance Threshold

  • AUTHORS: Marco Cuturi, Alexandre d'Aspremont

  • ABSTRACT: Starting from a sample path of a multivariate stochastic process, we study several techniques to isolate linear combinations of the variables with a maximal amount of mean reversion, while constraining the variance of the combination 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 a variant of the S-lemma. In finance, these methods can be used to isolate statistical arbitrage opportunities, i.e. mean reverting baskets with enough variance to overcome market friction. In a more general setting, mean reversion and its generalizations can also be used as a proxy for stationarity, while variance simply measures signal strength.

  • STATUS: Proceedings ICML 2013, pp 271-279.

  • HAL PREPRINT: hal-00939566

  • PAPER: Mean Reversion with a Variance Threshold in pdf