Maximum Likelihood Estimation for MA(1) Processes with a Root on or near the Unit Circle
This paper considers maximum likelihood estimation for the moving average parameter θ in an MA(1) model when θ is equal to or close to 1. A derivation of the limit distribution of the estimate θLM, defined as the largest of the local maximizers of the likelihood, is given here for the first time. Th...
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| Veröffentlicht in: | Econometric theory 1996-03, Vol.12 (1), p.1-29 |
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| container_title | Econometric theory |
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| creator | Davis, Richard A. Dunsmuir, William T.M. |
| description | This paper considers maximum likelihood estimation for the moving average parameter θ in an MA(1) model when θ is equal to or close to 1. A derivation of the limit distribution of the estimate θLM, defined as the largest of the local maximizers of the likelihood, is given here for the first time. The theory presented covers, in a unified way, cases where the true parameter is strictly inside the unit circle as well as the noninvertible case where it is on the unit circle. The asymptotic distribution of the maximum likelihood estimator subMLE is also described and shown to differ, but only slightly, from that of θLM. Of practical significance is the fact that the asymptotic distribution for either estimate is surprisingly accurate even for small sample sizes and for values of the moving average parameter considerably far from the unit circle. |
| doi_str_mv | 10.1017/S0266466600006423 |
| format | Article |
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A derivation of the limit distribution of the estimate θLM, defined as the largest of the local maximizers of the likelihood, is given here for the first time. The theory presented covers, in a unified way, cases where the true parameter is strictly inside the unit circle as well as the noninvertible case where it is on the unit circle. The asymptotic distribution of the maximum likelihood estimator subMLE is also described and shown to differ, but only slightly, from that of θLM. 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Theory</addtitle><description>This paper considers maximum likelihood estimation for the moving average parameter θ in an MA(1) model when θ is equal to or close to 1. A derivation of the limit distribution of the estimate θLM, defined as the largest of the local maximizers of the likelihood, is given here for the first time. The theory presented covers, in a unified way, cases where the true parameter is strictly inside the unit circle as well as the noninvertible case where it is on the unit circle. The asymptotic distribution of the maximum likelihood estimator subMLE is also described and shown to differ, but only slightly, from that of θLM. Of practical significance is the fact that the asymptotic distribution for either estimate is surprisingly accurate even for small sample sizes and for values of the moving average parameter considerably far from the unit circle.</description><subject>Approximation</subject><subject>Asymptotic theory</subject><subject>Econometrics</subject><subject>Estimators</subject><subject>Local maximum</subject><subject>Mathematical methods</subject><subject>Maximum likelihood estimation</subject><subject>Maximum likelihood estimators</subject><subject>Perceptron convergence procedure</subject><subject>Probability</subject><subject>Random variables</subject><subject>Sample size</subject><subject>Time series</subject><issn>0266-4666</issn><issn>1469-4360</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1996</creationdate><recordtype>article</recordtype><sourceid>K30</sourceid><recordid>eNp1kF1rFDEUhoMouFZ_gOBFQBC9GM1JJmdmLtu1rcLWr1rwLmRmTtxsZyY1ydL23zvLliKKuTkXz_OGl5ex5yDegoDq3bmQiCUiivlhKdUDtoASm6JUKB6yxQ4XO_6YPUlpIwTIplIL9uPM3vhxO_KVv6TBr0Po-XHKfrTZh4m7EPnZ4Wt4w7_E0FFKlPi1z2tu-bcQMp-V2ZjIRp7XxC8mn_nSx26gp-yRs0OiZ3f3gF2cHH9ffihWn08_Lg9XRVdilQvXktKi7h3pGpySmpqObCcRnO6doNZBAyA7VOBI1qpCUSKUdde2va5IqwP2av_vVQy_tpSyGX3qaBjsRGGbjKobBCmqWXz5l7gJ2zjN3QxoXQqEpmlmC_ZWF0NKkZy5ivMY8daAMLulzT9Lz5kX-8wm5RDvA0orWekdLvbYp0w399jGS4OVqrTB06_m6BxhiSefzPvZV3cV7NhG3_-kP5r-t8Rv0lSWTw</recordid><startdate>19960301</startdate><enddate>19960301</enddate><creator>Davis, Richard A.</creator><creator>Dunsmuir, William T.M.</creator><general>Cambridge University Press</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>HAGHG</scope><scope>IOIBA</scope><scope>K30</scope><scope>PAAUG</scope><scope>PAWHS</scope><scope>PAWZZ</scope><scope>PAXOH</scope><scope>PBHAV</scope><scope>PBQSW</scope><scope>PBYQZ</scope><scope>PCIWU</scope><scope>PCMID</scope><scope>PCZJX</scope><scope>PDGRG</scope><scope>PDWWI</scope><scope>PETMR</scope><scope>PFVGT</scope><scope>PGXDX</scope><scope>PIHIL</scope><scope>PISVA</scope><scope>PJCTQ</scope><scope>PJTMS</scope><scope>PLCHJ</scope><scope>PMHAD</scope><scope>PNQDJ</scope><scope>POUND</scope><scope>PPLAD</scope><scope>PQAPC</scope><scope>PQCAN</scope><scope>PQCMW</scope><scope>PQEME</scope><scope>PQHKH</scope><scope>PQMID</scope><scope>PQNCT</scope><scope>PQNET</scope><scope>PQSCT</scope><scope>PQSET</scope><scope>PSVJG</scope><scope>PVMQY</scope><scope>PZGFC</scope><scope>8BJ</scope><scope>FQK</scope><scope>JBE</scope></search><sort><creationdate>19960301</creationdate><title>Maximum Likelihood Estimation for MA(1) Processes with a Root on or near the Unit Circle</title><author>Davis, Richard A. ; Dunsmuir, William T.M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c467t-fbe3508dfe581f325e9ceac261f5df0ebf19112c631fe28376046148cbbd57e53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1996</creationdate><topic>Approximation</topic><topic>Asymptotic theory</topic><topic>Econometrics</topic><topic>Estimators</topic><topic>Local maximum</topic><topic>Mathematical methods</topic><topic>Maximum likelihood estimation</topic><topic>Maximum likelihood estimators</topic><topic>Perceptron convergence procedure</topic><topic>Probability</topic><topic>Random variables</topic><topic>Sample size</topic><topic>Time series</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Davis, Richard A.</creatorcontrib><creatorcontrib>Dunsmuir, William T.M.</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>Periodicals Index Online Segment 12</collection><collection>Periodicals Index Online Segment 29</collection><collection>Periodicals Index Online</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - West</collection><collection>Primary Sources Access (Plan D) - International</collection><collection>Primary Sources Access & Build (Plan A) - MEA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Midwest</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Northeast</collection><collection>Primary Sources Access (Plan D) - Southeast</collection><collection>Primary Sources Access (Plan D) - North Central</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Southeast</collection><collection>Primary Sources Access (Plan D) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - UK / I</collection><collection>Primary Sources Access (Plan D) - Canada</collection><collection>Primary Sources Access (Plan D) - EMEALA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - North Central</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - International</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - International</collection><collection>Primary Sources Access (Plan D) - West</collection><collection>Periodicals Index Online Segments 1-50</collection><collection>Primary Sources Access (Plan D) - APAC</collection><collection>Primary Sources Access (Plan D) - Midwest</collection><collection>Primary Sources Access (Plan D) - MEA</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - Canada</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - UK / I</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - EMEALA</collection><collection>Primary Sources Access & Build (Plan A) - APAC</collection><collection>Primary Sources Access & Build (Plan A) - Canada</collection><collection>Primary Sources Access & Build (Plan A) - West</collection><collection>Primary Sources Access & Build (Plan A) - EMEALA</collection><collection>Primary Sources Access (Plan D) - Northeast</collection><collection>Primary Sources Access & Build (Plan A) - Midwest</collection><collection>Primary Sources Access & Build (Plan A) - North Central</collection><collection>Primary Sources Access & Build (Plan A) - Northeast</collection><collection>Primary Sources Access & Build (Plan A) - South Central</collection><collection>Primary Sources Access & Build (Plan A) - Southeast</collection><collection>Primary Sources Access (Plan D) - UK / I</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - APAC</collection><collection>Primary Sources Access—Foundation Edition (Plan E) - MEA</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>Econometric theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Davis, Richard A.</au><au>Dunsmuir, William T.M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Maximum Likelihood Estimation for MA(1) Processes with a Root on or near the Unit Circle</atitle><jtitle>Econometric theory</jtitle><addtitle>Econom. Theory</addtitle><date>1996-03-01</date><risdate>1996</risdate><volume>12</volume><issue>1</issue><spage>1</spage><epage>29</epage><pages>1-29</pages><issn>0266-4666</issn><eissn>1469-4360</eissn><abstract>This paper considers maximum likelihood estimation for the moving average parameter θ in an MA(1) model when θ is equal to or close to 1. A derivation of the limit distribution of the estimate θLM, defined as the largest of the local maximizers of the likelihood, is given here for the first time. The theory presented covers, in a unified way, cases where the true parameter is strictly inside the unit circle as well as the noninvertible case where it is on the unit circle. The asymptotic distribution of the maximum likelihood estimator subMLE is also described and shown to differ, but only slightly, from that of θLM. Of practical significance is the fact that the asymptotic distribution for either estimate is surprisingly accurate even for small sample sizes and for values of the moving average parameter considerably far from the unit circle.</abstract><cop>New York, USA</cop><pub>Cambridge University Press</pub><doi>10.1017/S0266466600006423</doi><tpages>29</tpages></addata></record> |
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| ispartof | Econometric theory, 1996-03, Vol.12 (1), p.1-29 |
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| language | eng |
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| source | Periodicals Index Online; JSTOR Archive Collection A-Z Listing; Cambridge University Press Journals Complete |
| subjects | Approximation Asymptotic theory Econometrics Estimators Local maximum Mathematical methods Maximum likelihood estimation Maximum likelihood estimators Perceptron convergence procedure Probability Random variables Sample size Time series |
| title | Maximum Likelihood Estimation for MA(1) Processes with a Root on or near the Unit Circle |
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