Estimation of Copula Density Using the Wavelet Transform
This paper proposes a new method to estimate the copula density function using wavelet decomposition as a nonparametric method, to obtain more accurate results and address the issue of boundary effects that nonparametric estimation methods suffer from. The wavelet method is an automatic method for...
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University of Baghdad, College of Science for Women
2024-11-01
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| Series: | مجلة بغداد للعلوم |
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| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/9673 |
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| author | Fatimah Hashim Falhi Munaf Yousif Hmood |
| author_facet | Fatimah Hashim Falhi Munaf Yousif Hmood |
| author_sort | Fatimah Hashim Falhi |
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This paper proposes a new method to estimate the copula density function using wavelet decomposition as a nonparametric method, to obtain more accurate results and address the issue of boundary effects that nonparametric estimation methods suffer from. The wavelet method is an automatic method for dealing with boundary effects because it does not take into Consideration whether the time series is stationary or nonstationary. To estimate the copula density function, simulation was used to generate data using five different copula functions, such as Gaussian, Frank, Tawn, Rotation Tawn, and Joe copulas. With five different sample sizes at three positive correlation levels based on multiresolution. The results showed that in estimating the copula density function using the wavelet method when the correlation level = 0.7, the Gaussian copula ranked first, followed by the Frank copula, and the Joe copula ranked last. In the case of medium and weak correlation, the Tawn copula was in first place, followed by the Rotation Tawn copula, while Gaussian copula came in last place depending on the measures (Root Mean Square Error, Akiake Information Criteria, and Logarithm likelihood criteria). The real copula functions are shown through drawing (Contour plot) and (3D plot). In addition to the smoothing shapes for each of them using the wavelet method, it is clear from the circular shapes that the distribution of observations of the copula function estimated with the wavelet method was accurate at the edges, while it was less accurate at the center for Gaussian and Tawn functions.
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| format | Article |
| id | doaj-art-5af4e06a32154e4aa0f00af8af9c4e43 |
| institution | Kabale University |
| issn | 2078-8665 2411-7986 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | University of Baghdad, College of Science for Women |
| record_format | Article |
| series | مجلة بغداد للعلوم |
| spelling | doaj-art-5af4e06a32154e4aa0f00af8af9c4e432025-08-20T03:34:32ZengUniversity of Baghdad, College of Science for Womenمجلة بغداد للعلوم2078-86652411-79862024-11-01211110.21123/bsj.2024.9673Estimation of Copula Density Using the Wavelet TransformFatimah Hashim Falhi0https://orcid.org/0009-0008-1170-5635Munaf Yousif Hmood 1Department of Statistics , College of Administration and Economics , University of Basrah , Basrah, Iraq. Department of Statistics, College of Administration and Economics, University of Baghdad, Baghdad, Iraq. This paper proposes a new method to estimate the copula density function using wavelet decomposition as a nonparametric method, to obtain more accurate results and address the issue of boundary effects that nonparametric estimation methods suffer from. The wavelet method is an automatic method for dealing with boundary effects because it does not take into Consideration whether the time series is stationary or nonstationary. To estimate the copula density function, simulation was used to generate data using five different copula functions, such as Gaussian, Frank, Tawn, Rotation Tawn, and Joe copulas. With five different sample sizes at three positive correlation levels based on multiresolution. The results showed that in estimating the copula density function using the wavelet method when the correlation level = 0.7, the Gaussian copula ranked first, followed by the Frank copula, and the Joe copula ranked last. In the case of medium and weak correlation, the Tawn copula was in first place, followed by the Rotation Tawn copula, while Gaussian copula came in last place depending on the measures (Root Mean Square Error, Akiake Information Criteria, and Logarithm likelihood criteria). The real copula functions are shown through drawing (Contour plot) and (3D plot). In addition to the smoothing shapes for each of them using the wavelet method, it is clear from the circular shapes that the distribution of observations of the copula function estimated with the wavelet method was accurate at the edges, while it was less accurate at the center for Gaussian and Tawn functions. https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/9673Boundary Effects, Copula Function, Dependency, Multiresolution analysis, Wavelets |
| spellingShingle | Fatimah Hashim Falhi Munaf Yousif Hmood Estimation of Copula Density Using the Wavelet Transform مجلة بغداد للعلوم Boundary Effects, Copula Function, Dependency, Multiresolution analysis, Wavelets |
| title | Estimation of Copula Density Using the Wavelet Transform |
| title_full | Estimation of Copula Density Using the Wavelet Transform |
| title_fullStr | Estimation of Copula Density Using the Wavelet Transform |
| title_full_unstemmed | Estimation of Copula Density Using the Wavelet Transform |
| title_short | Estimation of Copula Density Using the Wavelet Transform |
| title_sort | estimation of copula density using the wavelet transform |
| topic | Boundary Effects, Copula Function, Dependency, Multiresolution analysis, Wavelets |
| url | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/9673 |
| work_keys_str_mv | AT fatimahhashimfalhi estimationofcopuladensityusingthewavelettransform AT munafyousifhmood estimationofcopuladensityusingthewavelettransform |