ASYMPTOTIC EFFICIENCY OF THE ORDINARY LEAST SQUARES ESTIMATOR FOR REGRESSIONS WITH UNSTABLE REGRESSORS
For regression models with general unstable regressors having characteristic roots on the unit circle and general stationary errors independent of the regressors, sufficient conditions are investigated under which the ordinary least squares estimator (OLSE) is asymptotically efficient in that it has...
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| Veröffentlicht in: | Econometric theory 2002-10, Vol.18 (5), p.1121-1138 |
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| container_title | Econometric theory |
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| creator | SHIN, DONG WAN OH, MAN SUK |
| description | For regression models with general unstable regressors having
characteristic roots on the unit circle and general stationary
errors independent of the regressors, sufficient conditions
are investigated under which the ordinary least squares estimator
(OLSE) is asymptotically efficient in that it has the same limiting
distribution as the generalized least squares estimator (GLSE)
under the same normalization. A key condition for the asymptotic
efficiency of the OLSE is that one multiplicity of a characteristic
root of the regressor process is strictly greater than the
multiplicities of the other roots. Under this condition, the
covariance matrix Γ of the errors and the regressor matrix
X are shown to satisfy a relationship
(ΓX = XC + V for some matrix
C) for V asymptotically dominated by X,
which is analogous to the condition (ΓX = XC
for some matrix C) for numerical equivalence of the
OLSE and the GLSE. |
| doi_str_mv | 10.1017/S0266466602185057 |
| format | Article |
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characteristic roots on the unit circle and general stationary
errors independent of the regressors, sufficient conditions
are investigated under which the ordinary least squares estimator
(OLSE) is asymptotically efficient in that it has the same limiting
distribution as the generalized least squares estimator (GLSE)
under the same normalization. A key condition for the asymptotic
efficiency of the OLSE is that one multiplicity of a characteristic
root of the regressor process is strictly greater than the
multiplicities of the other roots. Under this condition, the
covariance matrix Γ of the errors and the regressor matrix
X are shown to satisfy a relationship
(ΓX = XC + V for some matrix
C) for V asymptotically dominated by X,
which is analogous to the condition (ΓX = XC
for some matrix C) for numerical equivalence of the
OLSE and the GLSE.</description><identifier>ISSN: 0266-4666</identifier><identifier>EISSN: 1469-4360</identifier><identifier>DOI: 10.1017/S0266466602185057</identifier><language>eng</language><publisher>New York, USA: Cambridge University Press</publisher><subject>Covariance ; Covariance matrices ; Determinism ; Econometrics ; Efficiency ; Eigenvalues ; Equivalence ; Error ; Estimation ; Estimators ; Integers ; Least squares ; Least squares method ; Mathematical vectors ; Polynomials ; Regression analysis ; Stationary processes ; Time series ; Trends</subject><ispartof>Econometric theory, 2002-10, Vol.18 (5), p.1121-1138</ispartof><rights>2002 Cambridge University Press</rights><rights>Copyright 2002 Cambridge University Press</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c435t-1dec21025258440968bd86442517883322a2f23d7cf0124b6191fcc8e6b05d783</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/3533367$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0266466602185057/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,314,776,780,799,27901,27902,55603,57992,58225</link.rule.ids></links><search><creatorcontrib>SHIN, DONG WAN</creatorcontrib><creatorcontrib>OH, MAN SUK</creatorcontrib><title>ASYMPTOTIC EFFICIENCY OF THE ORDINARY LEAST SQUARES ESTIMATOR FOR REGRESSIONS WITH UNSTABLE REGRESSORS</title><title>Econometric theory</title><addtitle>Econom. Theory</addtitle><description>For regression models with general unstable regressors having
characteristic roots on the unit circle and general stationary
errors independent of the regressors, sufficient conditions
are investigated under which the ordinary least squares estimator
(OLSE) is asymptotically efficient in that it has the same limiting
distribution as the generalized least squares estimator (GLSE)
under the same normalization. A key condition for the asymptotic
efficiency of the OLSE is that one multiplicity of a characteristic
root of the regressor process is strictly greater than the
multiplicities of the other roots. Under this condition, the
covariance matrix Γ of the errors and the regressor matrix
X are shown to satisfy a relationship
(ΓX = XC + V for some matrix
C) for V asymptotically dominated by X,
which is analogous to the condition (ΓX = XC
for some matrix C) for numerical equivalence of the
OLSE and the GLSE.</description><subject>Covariance</subject><subject>Covariance matrices</subject><subject>Determinism</subject><subject>Econometrics</subject><subject>Efficiency</subject><subject>Eigenvalues</subject><subject>Equivalence</subject><subject>Error</subject><subject>Estimation</subject><subject>Estimators</subject><subject>Integers</subject><subject>Least squares</subject><subject>Least squares method</subject><subject>Mathematical vectors</subject><subject>Polynomials</subject><subject>Regression analysis</subject><subject>Stationary processes</subject><subject>Time series</subject><subject>Trends</subject><issn>0266-4666</issn><issn>1469-4360</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2002</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>BENPR</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kF9r2zAUxc1YYVm7DzDYg9jD3tzpjyXLj54nxwbXXi2FkSfh2PJIltSdlED77SuTroONPVwE93fO4egGwXsErxFE8WcJMWMRYwxixCmk8atggSKWhBFh8HWwmHE48zfBW-d2ECKcxGQRjKlc33xTjSozIPK8zEpRZ2vQ5EAVAjTt17JO2zWoRCoVkLertBUSCKnKm1Q1Lcj9tGLpl7Jsagm-l6oAq1qq9EslfpOmlVfBxdjtnXn3_F4Gq1yorAirZllmaRX2EaHHEA2mxwhiiimPIpgwvhk4iyJMUcw5IRh3eMRkiPvRfyDaMJSgse-5YRtIh5iTy-DTOffeTr9Oxh31Yet6s993d2Y6OU0SNCdBL_z4l3A3neyd76axT4Yxp4kXobOot5Nz1oz63m4PnX3UCOr57Pqfs3vPh7Nn546TfTEQSghhMw7PeOuO5uEFd_an9jSmmi1vdQHpUtVFriuvJ88VusPGbocf5k_R_5d4AmztkgU</recordid><startdate>200210</startdate><enddate>200210</enddate><creator>SHIN, DONG WAN</creator><creator>OH, MAN SUK</creator><general>Cambridge University Press</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>8BJ</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FQK</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>JBE</scope><scope>K60</scope><scope>K6~</scope><scope>L.-</scope><scope>M0C</scope><scope>M2O</scope><scope>MBDVC</scope><scope>PADUT</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PYYUZ</scope><scope>Q9U</scope></search><sort><creationdate>200210</creationdate><title>ASYMPTOTIC EFFICIENCY OF THE ORDINARY LEAST SQUARES ESTIMATOR FOR REGRESSIONS WITH UNSTABLE REGRESSORS</title><author>SHIN, DONG WAN ; OH, MAN SUK</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c435t-1dec21025258440968bd86442517883322a2f23d7cf0124b6191fcc8e6b05d783</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2002</creationdate><topic>Covariance</topic><topic>Covariance matrices</topic><topic>Determinism</topic><topic>Econometrics</topic><topic>Efficiency</topic><topic>Eigenvalues</topic><topic>Equivalence</topic><topic>Error</topic><topic>Estimation</topic><topic>Estimators</topic><topic>Integers</topic><topic>Least squares</topic><topic>Least squares method</topic><topic>Mathematical vectors</topic><topic>Polynomials</topic><topic>Regression analysis</topic><topic>Stationary processes</topic><topic>Time series</topic><topic>Trends</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>SHIN, DONG WAN</creatorcontrib><creatorcontrib>OH, MAN SUK</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>International Bibliography of the Social Sciences (IBSS)</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>International Bibliography of the Social Sciences</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>International Bibliography of the Social Sciences</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ABI/INFORM Global</collection><collection>Research Library</collection><collection>Research Library (Corporate)</collection><collection>Research Library China</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ABI/INFORM Collection China</collection><collection>ProQuest Central Basic</collection><jtitle>Econometric theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>SHIN, DONG WAN</au><au>OH, MAN SUK</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>ASYMPTOTIC EFFICIENCY OF THE ORDINARY LEAST SQUARES ESTIMATOR FOR REGRESSIONS WITH UNSTABLE REGRESSORS</atitle><jtitle>Econometric theory</jtitle><addtitle>Econom. Theory</addtitle><date>2002-10</date><risdate>2002</risdate><volume>18</volume><issue>5</issue><spage>1121</spage><epage>1138</epage><pages>1121-1138</pages><issn>0266-4666</issn><eissn>1469-4360</eissn><abstract>For regression models with general unstable regressors having
characteristic roots on the unit circle and general stationary
errors independent of the regressors, sufficient conditions
are investigated under which the ordinary least squares estimator
(OLSE) is asymptotically efficient in that it has the same limiting
distribution as the generalized least squares estimator (GLSE)
under the same normalization. A key condition for the asymptotic
efficiency of the OLSE is that one multiplicity of a characteristic
root of the regressor process is strictly greater than the
multiplicities of the other roots. Under this condition, the
covariance matrix Γ of the errors and the regressor matrix
X are shown to satisfy a relationship
(ΓX = XC + V for some matrix
C) for V asymptotically dominated by X,
which is analogous to the condition (ΓX = XC
for some matrix C) for numerical equivalence of the
OLSE and the GLSE.</abstract><cop>New York, USA</cop><pub>Cambridge University Press</pub><doi>10.1017/S0266466602185057</doi><tpages>18</tpages></addata></record> |
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| ispartof | Econometric theory, 2002-10, Vol.18 (5), p.1121-1138 |
| issn | 0266-4666 1469-4360 |
| language | eng |
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| source | Jstor Complete Legacy; Cambridge Journals |
| subjects | Covariance Covariance matrices Determinism Econometrics Efficiency Eigenvalues Equivalence Error Estimation Estimators Integers Least squares Least squares method Mathematical vectors Polynomials Regression analysis Stationary processes Time series Trends |
| title | ASYMPTOTIC EFFICIENCY OF THE ORDINARY LEAST SQUARES ESTIMATOR FOR REGRESSIONS WITH UNSTABLE REGRESSORS |
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