Weighted least squares approximate restricted likelihood estimation for vector autoregressive processes
We derive a weighted least squares approximate restricted likelihood estimator for a k-dimensional pth-order autoregressive model with intercept. Exact likelihood optimization of this model is generally infeasible due to the parameter space, which is complicated and high-dimensional, involving pk2 p...
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| Veröffentlicht in: | Biometrika 2010-03, Vol.97 (1), p.231-237 |
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| container_title | Biometrika |
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| creator | CHEN, WILLA W. DEO, ROHIT S. |
| description | We derive a weighted least squares approximate restricted likelihood estimator for a k-dimensional pth-order autoregressive model with intercept. Exact likelihood optimization of this model is generally infeasible due to the parameter space, which is complicated and high-dimensional, involving pk2 parameters. The weighted least squares estimator has significantly reduced bias and mean squared error than the ordinary least squares estimator for both stationary and nonstationary processes. Furthermore, at the unit root, the limiting distribution of the weighted least squares approximate restricted likelihood estimator is shown to be the zero-intercept Dickey–Fuller distribution, unlike the ordinary least squares with intercept estimator that has a different distribution with significantly higher bias. |
| doi_str_mv | 10.1093/biomet/asp071 |
| format | Article |
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Exact likelihood optimization of this model is generally infeasible due to the parameter space, which is complicated and high-dimensional, involving pk2 parameters. The weighted least squares estimator has significantly reduced bias and mean squared error than the ordinary least squares estimator for both stationary and nonstationary processes. Furthermore, at the unit root, the limiting distribution of the weighted least squares approximate restricted likelihood estimator is shown to be the zero-intercept Dickey–Fuller distribution, unlike the ordinary least squares with intercept estimator that has a different distribution with significantly higher bias.</description><identifier>ISSN: 0006-3444</identifier><identifier>ISSN: 1464-3510</identifier><identifier>EISSN: 1464-3510</identifier><identifier>EISSN: 0006-3444</identifier><identifier>DOI: 10.1093/biomet/asp071</identifier><identifier>CODEN: BIOKAX</identifier><language>eng</language><publisher>Oxford: Oxford University Press</publisher><subject>Applications ; Approximation ; Autoregressive models ; Autoregressive process ; Bias ; Biology, psychology, social sciences ; Calculus of variations and optimal control ; Coefficients ; Consistent estimators ; Estimating techniques ; Estimation bias ; Estimators ; Exact sciences and technology ; General topics ; Least squares ; Mathematical analysis ; Mathematics ; Maximum likelihood estimation ; Maximum likelihood estimators ; Miscellanea ; Numerical analysis ; Numerical analysis. Scientific computation ; Numerical methods in mathematical programming, optimization and calculus of variations ; Numerical methods in optimization and calculus of variations ; Optimization ; Probability and statistics ; Regression analysis ; Restricted maximum likelihood ; Root mean square errors ; Roots ; Sampling bias ; Sciences and techniques of general use ; Statistics ; Studies ; Unbiased estimating equation</subject><ispartof>Biometrika, 2010-03, Vol.97 (1), p.231-237</ispartof><rights>2010 Biometrika Trust</rights><rights>Oxford University Press © 2010 Biometrika Trust 2010</rights><rights>2015 INIST-CNRS</rights><rights>Copyright Oxford Publishing Limited(England) Mar 2010</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c487t-88e704ab54b66071376138bca2c103d65bd015a525fcbaa0a47fde79a73a30533</citedby><cites>FETCH-LOGICAL-c487t-88e704ab54b66071376138bca2c103d65bd015a525fcbaa0a47fde79a73a30533</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/27798911$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/27798911$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,776,780,799,828,1578,3994,27901,27902,57992,57996,58225,58229</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22598172$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttp://econpapers.repec.org/article/oupbiomet/v_3a97_3ay_3a2010_3ai_3a1_3ap_3a231-237.htm$$DView record in RePEc$$Hfree_for_read</backlink></links><search><creatorcontrib>CHEN, WILLA W.</creatorcontrib><creatorcontrib>DEO, ROHIT S.</creatorcontrib><title>Weighted least squares approximate restricted likelihood estimation for vector autoregressive processes</title><title>Biometrika</title><description>We derive a weighted least squares approximate restricted likelihood estimator for a k-dimensional pth-order autoregressive model with intercept. Exact likelihood optimization of this model is generally infeasible due to the parameter space, which is complicated and high-dimensional, involving pk2 parameters. The weighted least squares estimator has significantly reduced bias and mean squared error than the ordinary least squares estimator for both stationary and nonstationary processes. Furthermore, at the unit root, the limiting distribution of the weighted least squares approximate restricted likelihood estimator is shown to be the zero-intercept Dickey–Fuller distribution, unlike the ordinary least squares with intercept estimator that has a different distribution with significantly higher bias.</description><subject>Applications</subject><subject>Approximation</subject><subject>Autoregressive models</subject><subject>Autoregressive process</subject><subject>Bias</subject><subject>Biology, psychology, social sciences</subject><subject>Calculus of variations and optimal control</subject><subject>Coefficients</subject><subject>Consistent estimators</subject><subject>Estimating techniques</subject><subject>Estimation bias</subject><subject>Estimators</subject><subject>Exact sciences and technology</subject><subject>General topics</subject><subject>Least squares</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Maximum likelihood estimation</subject><subject>Maximum likelihood estimators</subject><subject>Miscellanea</subject><subject>Numerical analysis</subject><subject>Numerical analysis. Scientific computation</subject><subject>Numerical methods in mathematical programming, optimization and calculus of variations</subject><subject>Numerical methods in optimization and calculus of variations</subject><subject>Optimization</subject><subject>Probability and statistics</subject><subject>Regression analysis</subject><subject>Restricted maximum likelihood</subject><subject>Root mean square errors</subject><subject>Roots</subject><subject>Sampling bias</subject><subject>Sciences and techniques of general use</subject><subject>Statistics</subject><subject>Studies</subject><subject>Unbiased estimating equation</subject><issn>0006-3444</issn><issn>1464-3510</issn><issn>1464-3510</issn><issn>0006-3444</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><recordid>eNqFkctv00AQhy0EEqFw5IhkISFxcbvrfdlHqGhDVYkLqKiX1XgzTjZ1su6uHbX_PRMcJRIXDjOzj29_89gse8_ZOWe1uGh82OBwAalnhr_IZlxqWQjF2ctsxhjThZBSvs7epLTeb7XSs2x5h365GnCRdwhpyNPjCBFTDn0fw5PfwIA57Yfo3V_IP2DnVyEscjrcX_uwzdsQ8x26gQKM5HFJT5LfYU4ijpaY3mavWugSvjvEs-zX1befl_Pi9sf198svt4WTlRmKqkLDJDRKNlpTF8JoLqrGQek4EwutmgXjClSpWtcAMJCmXaCpwQgQTAlxln2edCnz40g12o1PDrsOthjGZDk3vNJGSk3ox3_QdRjjlqqzJeO61lVdElRMkIshpYit7SO1HZ8tZ3Y_dTtN3U5TJ_5m4iP26I5wGPsDt7MCakPumYzyMAqejJP1-yPBbSmMXQ0bEvt0qBCSg66NsHU-HUXLUtUVN-WpaUrz3_o-TOg60UedpIypq5rzU78-Dfh0vIf4YLURRtn573v79f5aM3F1Z-fiD75Vxjw</recordid><startdate>20100301</startdate><enddate>20100301</enddate><creator>CHEN, WILLA W.</creator><creator>DEO, ROHIT S.</creator><general>Oxford University Press</general><general>Biometrika Trust, University College London</general><general>Oxford University Press for Biometrika Trust</general><general>Oxford Publishing Limited (England)</general><scope>BSCLL</scope><scope>IQODW</scope><scope>DKI</scope><scope>X2L</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7QO</scope><scope>8FD</scope><scope>FR3</scope><scope>P64</scope></search><sort><creationdate>20100301</creationdate><title>Weighted least squares approximate restricted likelihood estimation for vector autoregressive processes</title><author>CHEN, WILLA W. ; DEO, ROHIT S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c487t-88e704ab54b66071376138bca2c103d65bd015a525fcbaa0a47fde79a73a30533</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Applications</topic><topic>Approximation</topic><topic>Autoregressive models</topic><topic>Autoregressive process</topic><topic>Bias</topic><topic>Biology, psychology, social sciences</topic><topic>Calculus of variations and optimal control</topic><topic>Coefficients</topic><topic>Consistent estimators</topic><topic>Estimating techniques</topic><topic>Estimation bias</topic><topic>Estimators</topic><topic>Exact sciences and technology</topic><topic>General topics</topic><topic>Least squares</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Maximum likelihood estimation</topic><topic>Maximum likelihood estimators</topic><topic>Miscellanea</topic><topic>Numerical analysis</topic><topic>Numerical analysis. Scientific computation</topic><topic>Numerical methods in mathematical programming, optimization and calculus of variations</topic><topic>Numerical methods in optimization and calculus of variations</topic><topic>Optimization</topic><topic>Probability and statistics</topic><topic>Regression analysis</topic><topic>Restricted maximum likelihood</topic><topic>Root mean square errors</topic><topic>Roots</topic><topic>Sampling bias</topic><topic>Sciences and techniques of general use</topic><topic>Statistics</topic><topic>Studies</topic><topic>Unbiased estimating equation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>CHEN, WILLA W.</creatorcontrib><creatorcontrib>DEO, ROHIT S.</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><collection>Biotechnology Research Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Biotechnology and BioEngineering Abstracts</collection><jtitle>Biometrika</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>CHEN, WILLA W.</au><au>DEO, ROHIT S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Weighted least squares approximate restricted likelihood estimation for vector autoregressive processes</atitle><jtitle>Biometrika</jtitle><date>2010-03-01</date><risdate>2010</risdate><volume>97</volume><issue>1</issue><spage>231</spage><epage>237</epage><pages>231-237</pages><issn>0006-3444</issn><issn>1464-3510</issn><eissn>1464-3510</eissn><eissn>0006-3444</eissn><coden>BIOKAX</coden><abstract>We derive a weighted least squares approximate restricted likelihood estimator for a k-dimensional pth-order autoregressive model with intercept. Exact likelihood optimization of this model is generally infeasible due to the parameter space, which is complicated and high-dimensional, involving pk2 parameters. The weighted least squares estimator has significantly reduced bias and mean squared error than the ordinary least squares estimator for both stationary and nonstationary processes. Furthermore, at the unit root, the limiting distribution of the weighted least squares approximate restricted likelihood estimator is shown to be the zero-intercept Dickey–Fuller distribution, unlike the ordinary least squares with intercept estimator that has a different distribution with significantly higher bias.</abstract><cop>Oxford</cop><pub>Oxford University Press</pub><doi>10.1093/biomet/asp071</doi><tpages>7</tpages></addata></record> |
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| source | Jstor Complete Legacy; Oxford University Press Journals All Titles (1996-Current); RePEc; Alma/SFX Local Collection; JSTOR Mathematics & Statistics |
| subjects | Applications Approximation Autoregressive models Autoregressive process Bias Biology, psychology, social sciences Calculus of variations and optimal control Coefficients Consistent estimators Estimating techniques Estimation bias Estimators Exact sciences and technology General topics Least squares Mathematical analysis Mathematics Maximum likelihood estimation Maximum likelihood estimators Miscellanea Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming, optimization and calculus of variations Numerical methods in optimization and calculus of variations Optimization Probability and statistics Regression analysis Restricted maximum likelihood Root mean square errors Roots Sampling bias Sciences and techniques of general use Statistics Studies Unbiased estimating equation |
| title | Weighted least squares approximate restricted likelihood estimation for vector autoregressive processes |
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