Scalable structural break detection

This paper deals with a statistical model fitting procedure for non-stationary time series. This procedure selects the parameters of a piecewise autoregressive model using the Minimum Description Length principle. The existing chromosome representation of the piecewise autoregressive model and its corresponding optimisation algorithm are improved. First, we show that our proposed chromosome representation better captures the intrinsic properties of the piecewise autoregressive model. Second, we apply an optimisation algorithm, the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), with which our setup converges faster to the optimal fit. Our proposed method achieves at least one order of magnitude performance improvement compared to the existing solution.

[1]  A. Aue,et al.  Break detection in the covariance structure of multivariate time series models , 2009, 0911.3796.

[2]  Jorma Rissanen,et al.  Order estimation by accumulated prediction errors , 1986 .

[3]  Patrice Marcotte,et al.  An overview of bilevel optimization , 2007, Ann. Oper. Res..

[4]  J. Rissanen,et al.  Conditional NML Universal Models , 2007, 2007 Information Theory and Applications Workshop.

[5]  B. Efron,et al.  Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information , 1978 .

[6]  H. Ombao,et al.  SLEX Analysis of Multivariate Nonstationary Time Series , 2005 .

[7]  B. Darkhovski.  Nonparametric methods in change-point problems: a general approach and some concrete algorithms , 1994 .

[8]  Michèle Sebag,et al.  Towards Non-Stationary Grid Models , 2011, Journal of Grid Computing.

[9]  J. Raz,et al.  Automatic Statistical Analysis of Bivariate Nonstationary Time Series , 2001 .

[10]  Kenji Yamanishi,et al.  Dynamic Model Selection With its Applications to Novelty Detection , 2007, IEEE Transactions on Information Theory.

[11]  Richard A. Davis,et al.  Structural Break Estimation for Nonstationary Time Series Models , 2006 .

[12]  P. Perron,et al.  Estimating and testing linear models with multiple structural changes , 1995 .

[13]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[14]  Pedro Larrañaga,et al.  Towards a New Evolutionary Computation - Advances in the Estimation of Distribution Algorithms , 2006, Towards a New Evolutionary Computation.

[15]  Michèle Basseville,et al.  Detection of abrupt changes: theory and application , 1993 .

[16]  Michèle Basseville,et al.  Detection of Abrupt Changes: Theory and Applications. , 1995 .

[17]  Jorma Rissanen,et al.  Estimation of AR and ARMA models by stochastic complexity , 2006 .

[18]  P. Perron,et al.  Econometric Theory and Practice: Multiple Structural Change Models: A Simulation Analysis , 2006 .

[19]  Michèle Sebag,et al.  Discovering Piecewise Linear Models of Grid Workload , 2010, 2010 10th IEEE/ACM International Conference on Cluster, Cloud and Grid Computing.

[20]  Nikolaus Hansen,et al.  The CMA Evolution Strategy: A Comparing Review , 2006, Towards a New Evolutionary Computation.

[21]  B. Brodsky,et al.  Nonparametric Methods in Change Point Problems , 1993 .

[22]  Jorma Rissanen,et al.  Minimum Description Length Principle , 2010, Encyclopedia of Machine Learning.

[23]  Raymond Ros,et al.  A Simple Modification in CMA-ES Achieving Linear Time and Space Complexity , 2008, PPSN.

[24]  Nikolaus Hansen,et al.  A restart CMA evolution strategy with increasing population size , 2005, 2005 IEEE Congress on Evolutionary Computation.