Optimal Markov Approximations and Generalized Embeddings Export

@article{citeulike:3111862, abstract = {Based on information theory, we present a method to determine an optimal Markov approximation for modelling and prediction from time series data. The method finds a balance between minimal modelling errors by taking as much as possible memory into account and minimal statistical errors by working in embedding spaces of rather small dimension. A key ingredient is an estimate of the statistical error of entropy estimates. The method is illustrated with several examples and the consequences for prediction are evaluated by means of the root mean squard prediction error for point prediction.}, archivePrefix = {arXiv}, author = {Holstein, Detlef and Kantz, Holger}, citeulike-article-id = {3111862}, citeulike-linkout-0 = {http://arxiv.org/abs/0808.1513}, citeulike-linkout-1 = {http://arxiv.org/pdf/0808.1513}, day = {11}, eprint = {0808.1513}, keywords = {chaos, markov}, month = {Aug}, posted-at = {2008-08-12 14:01:14}, priority = {2}, title = {Optimal Markov Approximations and Generalized Embeddings}, url = {http://arxiv.org/abs/0808.1513}, year = {2008} }

TY - JOUR ID - citeulike:3111862 L3 - citeulike-article-id:3111862 N2 - Based on information theory, we present a method to determine an optimal Markov approximation for modelling and prediction from time series data. The method finds a balance between minimal modelling errors by taking as much as possible memory into account and minimal statistical errors by working in embedding spaces of rather small dimension. A key ingredient is an estimate of the statistical error of entropy estimates. The method is illustrated with several examples and the consequences for prediction are evaluated by means of the root mean squard prediction error for point prediction. TI - Optimal Markov Approximations and Generalized Embeddings KW - chaos KW - markov AU - Holstein, Detlef AU - Kantz, Holger PY - 2008/Aug/11/ UR - http://arxiv.org/abs/0808.1513 ER -