Likelihood analysis of a first order autoregressive model with exponential innovations
This paper derives the exact distribution of the maximum likelihood estimator of a first-order linear autoregression with an exponential disturbance term. We also show that, even if the process is stationary, the estimator is T-consistent, where T is the sample size. In the unit root case, the estim...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Blackwell Publishing
2003
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| _version_ | 1826298711340220416 |
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| author | Shephard, N Nielsen, B |
| author_facet | Shephard, N Nielsen, B |
| author_sort | Shephard, N |
| collection | OXFORD |
| description | This paper derives the exact distribution of the maximum likelihood estimator of a first-order linear autoregression with an exponential disturbance term. We also show that, even if the process is stationary, the estimator is T-consistent, where T is the sample size. In the unit root case, the estimator is T2-consistent, while, in the explosive case, the estimator is ρT-consistent. Further, the likelihood ratio test statistic for a simple hypothesis on the autoregressive parameter is asymptotically uniform for all values of the parameter. |
| first_indexed | 2024-03-07T04:51:00Z |
| format | Journal article |
| id | oxford-uuid:d4f26112-a85b-468c-8cf4-a3136f5184ec |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:51:00Z |
| publishDate | 2003 |
| publisher | Blackwell Publishing |
| record_format | dspace |
| spelling | oxford-uuid:d4f26112-a85b-468c-8cf4-a3136f5184ec2022-03-27T08:22:28ZLikelihood analysis of a first order autoregressive model with exponential innovationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d4f26112-a85b-468c-8cf4-a3136f5184ecEnglishDepartment of Economics - ePrintsBlackwell Publishing2003Shephard, NNielsen, BThis paper derives the exact distribution of the maximum likelihood estimator of a first-order linear autoregression with an exponential disturbance term. We also show that, even if the process is stationary, the estimator is T-consistent, where T is the sample size. In the unit root case, the estimator is T2-consistent, while, in the explosive case, the estimator is ρT-consistent. Further, the likelihood ratio test statistic for a simple hypothesis on the autoregressive parameter is asymptotically uniform for all values of the parameter. |
| spellingShingle | Shephard, N Nielsen, B Likelihood analysis of a first order autoregressive model with exponential innovations |
| title | Likelihood analysis of a first order autoregressive model with exponential innovations |
| title_full | Likelihood analysis of a first order autoregressive model with exponential innovations |
| title_fullStr | Likelihood analysis of a first order autoregressive model with exponential innovations |
| title_full_unstemmed | Likelihood analysis of a first order autoregressive model with exponential innovations |
| title_short | Likelihood analysis of a first order autoregressive model with exponential innovations |
| title_sort | likelihood analysis of a first order autoregressive model with exponential innovations |
| work_keys_str_mv | AT shephardn likelihoodanalysisofafirstorderautoregressivemodelwithexponentialinnovations AT nielsenb likelihoodanalysisofafirstorderautoregressivemodelwithexponentialinnovations |