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Oracle inequalities for high dimensional vector autoregressions
This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO in stationary vector autoregressive models. These inequalities are used to establish consistency of the LASSO even when the number of parameters is of a much larger order of magnit...
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| Published in: | Journal of econometrics 2015-06, Vol.186 (2), p.325-344 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c551t-e005cad6c2d720f7c5f02fa80cdee294e92665896deedc9dcc4177b8cc8264053 |
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| cites | cdi_FETCH-LOGICAL-c551t-e005cad6c2d720f7c5f02fa80cdee294e92665896deedc9dcc4177b8cc8264053 |
| container_end_page | 344 |
| container_issue | 2 |
| container_start_page | 325 |
| container_title | Journal of econometrics |
| container_volume | 186 |
| creator | Kock, Anders Bredahl Callot, Laurent |
| description | This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO in stationary vector autoregressive models. These inequalities are used to establish consistency of the LASSO even when the number of parameters is of a much larger order of magnitude than the sample size. We also state conditions under which no relevant variables are excluded.
Next, non-asymptotic probabilities are given for the adaptive LASSO to select the correct sparsity pattern. We then provide conditions under which the adaptive LASSO reveals the correct sparsity pattern asymptotically. We establish that the estimates of the non-zero coefficients are asymptotically equivalent to the oracle assisted least squares estimator. This is used to show that the rate of convergence of the estimates of the non-zero coefficients is identical to the one of least squares only including the relevant covariates. |
| doi_str_mv | 10.1016/j.jeconom.2015.02.013 |
| format | article |
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Next, non-asymptotic probabilities are given for the adaptive LASSO to select the correct sparsity pattern. We then provide conditions under which the adaptive LASSO reveals the correct sparsity pattern asymptotically. We establish that the estimates of the non-zero coefficients are asymptotically equivalent to the oracle assisted least squares estimator. This is used to show that the rate of convergence of the estimates of the non-zero coefficients is identical to the one of least squares only including the relevant covariates.</description><identifier>ISSN: 0304-4076</identifier><identifier>EISSN: 1872-6895</identifier><identifier>DOI: 10.1016/j.jeconom.2015.02.013</identifier><identifier>CODEN: JECMB6</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Adaptive LASSO ; Asymptotic methods ; Coefficients ; Convergence ; Econometrics ; Economic theory ; Estimating techniques ; Estimation ; High-dimensional data ; Inequality ; LASSO ; Oracle inequality ; Probability ; Regression analysis ; Sparsity ; Studies ; VAR ; Vector-autoregressive models</subject><ispartof>Journal of econometrics, 2015-06, Vol.186 (2), p.325-344</ispartof><rights>2015 Elsevier B.V.</rights><rights>Copyright Elsevier Sequoia S.A. Jun 2015</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c551t-e005cad6c2d720f7c5f02fa80cdee294e92665896deedc9dcc4177b8cc8264053</citedby><cites>FETCH-LOGICAL-c551t-e005cad6c2d720f7c5f02fa80cdee294e92665896deedc9dcc4177b8cc8264053</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0304407615000378$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3460,3564,27924,27925,33223,33224,45992,46003</link.rule.ids></links><search><creatorcontrib>Kock, Anders Bredahl</creatorcontrib><creatorcontrib>Callot, Laurent</creatorcontrib><title>Oracle inequalities for high dimensional vector autoregressions</title><title>Journal of econometrics</title><description>This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO in stationary vector autoregressive models. These inequalities are used to establish consistency of the LASSO even when the number of parameters is of a much larger order of magnitude than the sample size. We also state conditions under which no relevant variables are excluded.
Next, non-asymptotic probabilities are given for the adaptive LASSO to select the correct sparsity pattern. We then provide conditions under which the adaptive LASSO reveals the correct sparsity pattern asymptotically. We establish that the estimates of the non-zero coefficients are asymptotically equivalent to the oracle assisted least squares estimator. This is used to show that the rate of convergence of the estimates of the non-zero coefficients is identical to the one of least squares only including the relevant covariates.</description><subject>Adaptive LASSO</subject><subject>Asymptotic methods</subject><subject>Coefficients</subject><subject>Convergence</subject><subject>Econometrics</subject><subject>Economic theory</subject><subject>Estimating techniques</subject><subject>Estimation</subject><subject>High-dimensional data</subject><subject>Inequality</subject><subject>LASSO</subject><subject>Oracle inequality</subject><subject>Probability</subject><subject>Regression analysis</subject><subject>Sparsity</subject><subject>Studies</subject><subject>VAR</subject><subject>Vector-autoregressive models</subject><issn>0304-4076</issn><issn>1872-6895</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>8BJ</sourceid><recordid>eNqFkEtrwzAMgM3YYN3jJwwCu-ySTHZsJzmVUfaCQS_b2XiK0jmk8Wo3hf37ubSnXXaRkfgkWR9jNxwKDlzf90VP6Ee_LgRwVYAogJcnbMbrSuS6btQpm0EJMpdQ6XN2EWMPAErW5YzNl8HiQJkbaTPZwW0dxazzIftyq6-sdWsao_OjHbId4TbV7ZQirQLFfT1esbPODpGuj-8l-3h6fF-85G_L59fFw1uOSvFtTmkf2lajaCsBXYWqA9HZGrAlEo2kRmit6kantMWmRZS8qj5rxFpoCaq8ZHeHud_BbyaKW7N2EWkY7Eh-iobrRjWNFFIk9PYP2vsppBP2VC3L9AGQiVIHCoOPMVBnvoNb2_BjOJi9VtObo1az12pAmKQ19c0PfZSu3TkKJqKjEal1IRkyrXf_TPgFCu2DzQ</recordid><startdate>20150601</startdate><enddate>20150601</enddate><creator>Kock, Anders Bredahl</creator><creator>Callot, Laurent</creator><general>Elsevier B.V</general><general>Elsevier Sequoia S.A</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8BJ</scope><scope>FQK</scope><scope>JBE</scope></search><sort><creationdate>20150601</creationdate><title>Oracle inequalities for high dimensional vector autoregressions</title><author>Kock, Anders Bredahl ; Callot, Laurent</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c551t-e005cad6c2d720f7c5f02fa80cdee294e92665896deedc9dcc4177b8cc8264053</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Adaptive LASSO</topic><topic>Asymptotic methods</topic><topic>Coefficients</topic><topic>Convergence</topic><topic>Econometrics</topic><topic>Economic theory</topic><topic>Estimating techniques</topic><topic>Estimation</topic><topic>High-dimensional data</topic><topic>Inequality</topic><topic>LASSO</topic><topic>Oracle inequality</topic><topic>Probability</topic><topic>Regression analysis</topic><topic>Sparsity</topic><topic>Studies</topic><topic>VAR</topic><topic>Vector-autoregressive models</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kock, Anders Bredahl</creatorcontrib><creatorcontrib>Callot, Laurent</creatorcontrib><collection>CrossRef</collection><collection>International Bibliography of the Social Sciences (IBSS)</collection><collection>International Bibliography of the Social Sciences</collection><collection>International Bibliography of the Social Sciences</collection><jtitle>Journal of econometrics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kock, Anders Bredahl</au><au>Callot, Laurent</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Oracle inequalities for high dimensional vector autoregressions</atitle><jtitle>Journal of econometrics</jtitle><date>2015-06-01</date><risdate>2015</risdate><volume>186</volume><issue>2</issue><spage>325</spage><epage>344</epage><pages>325-344</pages><issn>0304-4076</issn><eissn>1872-6895</eissn><coden>JECMB6</coden><abstract>This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO in stationary vector autoregressive models. These inequalities are used to establish consistency of the LASSO even when the number of parameters is of a much larger order of magnitude than the sample size. We also state conditions under which no relevant variables are excluded.
Next, non-asymptotic probabilities are given for the adaptive LASSO to select the correct sparsity pattern. We then provide conditions under which the adaptive LASSO reveals the correct sparsity pattern asymptotically. We establish that the estimates of the non-zero coefficients are asymptotically equivalent to the oracle assisted least squares estimator. This is used to show that the rate of convergence of the estimates of the non-zero coefficients is identical to the one of least squares only including the relevant covariates.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.jeconom.2015.02.013</doi><tpages>20</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Journal of econometrics, 2015-06, Vol.186 (2), p.325-344 |
| issn | 0304-4076 1872-6895 |
| language | eng |
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| source | International Bibliography of the Social Sciences (IBSS); ScienceDirect Freedom Collection 2022-2024; Elsevier SD Backfile Economics; Backfile Package - Mathematics (Legacy) [YMT] |
| subjects | Adaptive LASSO Asymptotic methods Coefficients Convergence Econometrics Economic theory Estimating techniques Estimation High-dimensional data Inequality LASSO Oracle inequality Probability Regression analysis Sparsity Studies VAR Vector-autoregressive models |
| title | Oracle inequalities for high dimensional vector autoregressions |
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