Mean Reversion with a Variance Threshold

Marco Cuturi; Alexandre D’Aspremont

Mean Reversion with a Variance Threshold

Marco Cuturi, Alexandre D’Aspremont ;

Proceedings of the 30th International Conference on Machine Learning, PMLR 28(3):271-279, 2013.

Abstract

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 \mathcalS-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.

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@InProceedings{pmlr-v28-cuturi13, title = {Mean Reversion with a Variance Threshold}, author = {Marco Cuturi and Alexandre D’Aspremont}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {271--279}, year = {2013}, editor = {Sanjoy Dasgupta and David McAllester}, volume = {28}, number = {3}, series = {Proceedings of Machine Learning Research}, address = {Atlanta, Georgia, USA}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v28/cuturi13.pdf}, url = {http://proceedings.mlr.press/v28/cuturi13.html}, abstract = {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 \mathcalS-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.} }

%0 Conference Paper %T Mean Reversion with a Variance Threshold %A Marco Cuturi %A Alexandre D’Aspremont %B Proceedings of the 30th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Sanjoy Dasgupta %E David McAllester %F pmlr-v28-cuturi13 %I PMLR %J Proceedings of Machine Learning Research %P 271--279 %U http://proceedings.mlr.press %V 28 %N 3 %W PMLR %X 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 \mathcalS-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.

TY - CPAPER TI - Mean Reversion with a Variance Threshold AU - Marco Cuturi AU - Alexandre D’Aspremont BT - Proceedings of the 30th International Conference on Machine Learning PY - 2013/02/13 DA - 2013/02/13 ED - Sanjoy Dasgupta ED - David McAllester ID - pmlr-v28-cuturi13 PB - PMLR SP - 271 DP - PMLR EP - 279 L1 - http://proceedings.mlr.press/v28/cuturi13.pdf UR - http://proceedings.mlr.press/v28/cuturi13.html AB - 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 \mathcalS-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. ER -