Comparison Between the Exact Likelihood and Whittle Likelihood for Moving Average Processes
For Gaussian stationary processes, the likelihood functions include the inverse and determinant of the covariance matrices, and Whittle likelihood is considered as a standard technique to avoid expensive matrix determinant and inversions under large sample size. In this paper, we investigate the dif...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Bologna
2022-07-01
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| Series: | Statistica |
| Subjects: | |
| Online Access: | https://rivista-statistica.unibo.it/article/view/13609 |
| _version_ | 1811225449706029056 |
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| author | Xiaofei Xu Zhengze Li Masanobu Taniguchi |
| author_facet | Xiaofei Xu Zhengze Li Masanobu Taniguchi |
| author_sort | Xiaofei Xu |
| collection | DOAJ |
| description | For Gaussian stationary processes, the likelihood functions include the inverse and determinant of the covariance matrices, and Whittle likelihood is considered as a standard technique to avoid expensive matrix determinant and inversions under large sample size. In this paper, we investigate the difference between the exact likelihood and Whittle likelihood with finite sample size for moving average processes of order one. We elucidate the theoretical expressions of two likelihood functions and their expectations and evaluate the performance between exact likelihood and Whittle likelihood numerically. We find that the exact likelihood and Whittle likelihood perform similarly when the true value of parameter is close to zero, while the difference becomes large and Whittle estimator performs poorly when absolute value of parameter gets close to one. This is an important warning when we use the Whittle likelihood and estimator if the parameter of moving average process nears the boundary of parameter space. |
| first_indexed | 2024-04-12T09:07:23Z |
| format | Article |
| id | doaj.art-9a4bdb0b67db4d00b206cfe1294d2f06 |
| institution | Directory Open Access Journal |
| issn | 0390-590X 1973-2201 |
| language | English |
| last_indexed | 2024-04-12T09:07:23Z |
| publishDate | 2022-07-01 |
| publisher | University of Bologna |
| record_format | Article |
| series | Statistica |
| spelling | doaj.art-9a4bdb0b67db4d00b206cfe1294d2f062022-12-22T03:39:04ZengUniversity of BolognaStatistica0390-590X1973-22012022-07-0182131310.6092/issn.1973-2201/1360911928Comparison Between the Exact Likelihood and Whittle Likelihood for Moving Average ProcessesXiaofei Xu0Zhengze Li1Masanobu Taniguchi2Waseda UniversityWaseda UniversityWaseda UniversityFor Gaussian stationary processes, the likelihood functions include the inverse and determinant of the covariance matrices, and Whittle likelihood is considered as a standard technique to avoid expensive matrix determinant and inversions under large sample size. In this paper, we investigate the difference between the exact likelihood and Whittle likelihood with finite sample size for moving average processes of order one. We elucidate the theoretical expressions of two likelihood functions and their expectations and evaluate the performance between exact likelihood and Whittle likelihood numerically. We find that the exact likelihood and Whittle likelihood perform similarly when the true value of parameter is close to zero, while the difference becomes large and Whittle estimator performs poorly when absolute value of parameter gets close to one. This is an important warning when we use the Whittle likelihood and estimator if the parameter of moving average process nears the boundary of parameter space.https://rivista-statistica.unibo.it/article/view/13609gaussian stationary processspectral densitylikelihood functionwhittle likelihoodmoving average process |
| spellingShingle | Xiaofei Xu Zhengze Li Masanobu Taniguchi Comparison Between the Exact Likelihood and Whittle Likelihood for Moving Average Processes Statistica gaussian stationary process spectral density likelihood function whittle likelihood moving average process |
| title | Comparison Between the Exact Likelihood and Whittle Likelihood for Moving Average Processes |
| title_full | Comparison Between the Exact Likelihood and Whittle Likelihood for Moving Average Processes |
| title_fullStr | Comparison Between the Exact Likelihood and Whittle Likelihood for Moving Average Processes |
| title_full_unstemmed | Comparison Between the Exact Likelihood and Whittle Likelihood for Moving Average Processes |
| title_short | Comparison Between the Exact Likelihood and Whittle Likelihood for Moving Average Processes |
| title_sort | comparison between the exact likelihood and whittle likelihood for moving average processes |
| topic | gaussian stationary process spectral density likelihood function whittle likelihood moving average process |
| url | https://rivista-statistica.unibo.it/article/view/13609 |
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