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A Direct Estimation of High Dimensional Stationary Vector Autoregressions

Author(s): Han, Fang; Lu, Huanran; Liu, Han

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dc.contributor.authorHan, Fang-
dc.contributor.authorLu, Huanran-
dc.contributor.authorLiu, Han-
dc.date.accessioned2020-03-30T18:52:33Z-
dc.date.available2020-03-30T18:52:33Z-
dc.date.issued2015-12-01en_US
dc.identifier.citationHan, F, Lu, H, Liu, H. (2015). A direct estimation of high dimensional stationary vector autoregressions. Journal of Machine Learning Research, 16 (3115 - 3150). Retrieved from http://jmlr.org/papers/v16/han15a.htmlen_US
dc.identifier.issn1532-4435-
dc.identifier.urihttp://jmlr.org/papers/v16/han15a.html-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr11j4s-
dc.description.abstract© 2015 Fang Han, Huanran Lu, and Han Liu. The vector autoregressive (VAR) model is a powerful tool in learning complex time series and has been exploited in many fields. The VAR model poses some unique challenges to researchers: On one hand, the dimensionality, introduced by incorporating multiple numbers of time series and adding the order of the vector autoregression, is usually much higher than the time series length; On the other hand, the temporal dependence structure naturally present in the VAR model gives rise to extra difficulties in data analysis. The regular way in cracking the VAR model is via "least squares" and usually involves adding different penalty terms (e.g., ridge or lasso penalty) in handling high dimensionality. In this manuscript, we propose an alternative way in estimating the VAR model. The main idea is, via exploiting the temporal dependence structure, formulating the estimating problem to a linear program. There is instant advantage of the proposed approach over the lassotype estimators: The estimation equation can be decomposed to multiple sub-equations and accordingly can be solved efficiently using parallel computing. Besides that, we also bring new theoretical insights into the VAR model analysis. So far the theoretical results developed in high dimensions (e.g., Song and Bickel, 2011 and Kock and Callot, 2015) are based on stringent assumptions that are not transparent. Our results, on the other hand, show that the spectral norms of the transition matrices play an important role in estimation accuracy and build estimation and prediction consistency accordingly. Moreover, we provide some experiments on both synthetic and real-world equity data. We show that there are empirical advantages of our method over the lasso-type estimators in parameter estimation and forecasting.en_US
dc.format.extent3115 - 3150en_US
dc.language.isoen_USen_US
dc.relation.ispartofJournal of Machine Learning Researchen_US
dc.rightsFinal published version. This is an open access article.en_US
dc.titleA Direct Estimation of High Dimensional Stationary Vector Autoregressionsen_US
dc.typeJournal Articleen_US
dc.identifier.eissn1533-7928-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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