Impact of dependence on parameter estimates of autoregressive process with Gumbel distributed innovation
Recent studies have shown that independent identical distributed Gaussianrandom variables is not suitable for modelling extreme values observed during extremal events. However, many real life data on extreme values are dependent and stationary rather than the conventional independent identically dis...
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| Format: | Article |
| Language: | English |
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Department of Mathematics, Universiti Teknologi Malaysia
2018
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| Online Access: | http://psasir.upm.edu.my/id/eprint/74562/1/Impact%20of%20dependence%20on%20parameter%20estimates%20of%20autoregressive%20process%20with%20Gumbel%20distributed%20innovation.pdf |
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| author | Samuel, Bako Sunday Adam, Mohd Bakri Fitrianto, Anwar |
| author_facet | Samuel, Bako Sunday Adam, Mohd Bakri Fitrianto, Anwar |
| author_sort | Samuel, Bako Sunday |
| collection | UPM |
| description | Recent studies have shown that independent identical distributed Gaussianrandom variables is not suitable for modelling extreme values observed during extremal events. However, many real life data on extreme values are dependent and stationary rather than the conventional independent identically distributed data. We propose a sta-tionary autoregressive (AR) process with Gumbel distributed innovation and characterise the short-term dependence among maxima of an (AR) process over a range of sample sizes with varying degrees of dependence. We estimate the maximum likelihood of the parameters of the Gumbel AR process and its residuals, and evaluate the performance of the parameter estimates. The AR process is fitted to the Gumbel-generalised Pareto(GPD) distribution and we evaluate the performance of the parameter estimates fitted to the cluster maxima and the original series. Ignoring the effect of dependence leads tooverestimation of the location parameter of the Gumbel-AR (1) process. The estimate of the location parameter of the AR process using the residuals gives a better estimate.Estimate of the scale parameter perform marginally better for the original series than the residual estimate. The degree of clustering increases as dependence is enhance for the AR process. The Gumbel-AR(1) fitted to the threshold exceedances shows that the estimates of the scale and shape parameters fitted to the cluster maxima perform better as sample size increases, however, ignoring the effect of dependence lead to an under estimation ofthe parameter estimates of the scale parameter. The shape parameter of the original series gives a superior estimate compare to the threshold excesses fitted to the Gumbel distributed Generalised Pareto ditribution. |
| first_indexed | 2024-03-06T10:13:19Z |
| format | Article |
| id | upm.eprints-74562 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T10:13:19Z |
| publishDate | 2018 |
| publisher | Department of Mathematics, Universiti Teknologi Malaysia |
| record_format | dspace |
| spelling | upm.eprints-745622019-10-15T03:40:25Z http://psasir.upm.edu.my/id/eprint/74562/ Impact of dependence on parameter estimates of autoregressive process with Gumbel distributed innovation Samuel, Bako Sunday Adam, Mohd Bakri Fitrianto, Anwar Recent studies have shown that independent identical distributed Gaussianrandom variables is not suitable for modelling extreme values observed during extremal events. However, many real life data on extreme values are dependent and stationary rather than the conventional independent identically distributed data. We propose a sta-tionary autoregressive (AR) process with Gumbel distributed innovation and characterise the short-term dependence among maxima of an (AR) process over a range of sample sizes with varying degrees of dependence. We estimate the maximum likelihood of the parameters of the Gumbel AR process and its residuals, and evaluate the performance of the parameter estimates. The AR process is fitted to the Gumbel-generalised Pareto(GPD) distribution and we evaluate the performance of the parameter estimates fitted to the cluster maxima and the original series. Ignoring the effect of dependence leads tooverestimation of the location parameter of the Gumbel-AR (1) process. The estimate of the location parameter of the AR process using the residuals gives a better estimate.Estimate of the scale parameter perform marginally better for the original series than the residual estimate. The degree of clustering increases as dependence is enhance for the AR process. The Gumbel-AR(1) fitted to the threshold exceedances shows that the estimates of the scale and shape parameters fitted to the cluster maxima perform better as sample size increases, however, ignoring the effect of dependence lead to an under estimation ofthe parameter estimates of the scale parameter. The shape parameter of the original series gives a superior estimate compare to the threshold excesses fitted to the Gumbel distributed Generalised Pareto ditribution. Department of Mathematics, Universiti Teknologi Malaysia 2018-12-01 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/74562/1/Impact%20of%20dependence%20on%20parameter%20estimates%20of%20autoregressive%20process%20with%20Gumbel%20distributed%20innovation.pdf Samuel, Bako Sunday and Adam, Mohd Bakri and Fitrianto, Anwar (2018) Impact of dependence on parameter estimates of autoregressive process with Gumbel distributed innovation. MATEMATIKA: Malaysian Journal of Industrial and Applied Mathematics (MJIAM), 34 (2). 365 - 380. ISSN 0127-8274; ESSN: 0127-9602 https://matematika.utm.my/index.php/matematika/article/view/941 10.11113/matematika.v34.n2.941 |
| spellingShingle | Samuel, Bako Sunday Adam, Mohd Bakri Fitrianto, Anwar Impact of dependence on parameter estimates of autoregressive process with Gumbel distributed innovation |
| title | Impact of dependence on parameter estimates of autoregressive process with Gumbel distributed innovation |
| title_full | Impact of dependence on parameter estimates of autoregressive process with Gumbel distributed innovation |
| title_fullStr | Impact of dependence on parameter estimates of autoregressive process with Gumbel distributed innovation |
| title_full_unstemmed | Impact of dependence on parameter estimates of autoregressive process with Gumbel distributed innovation |
| title_short | Impact of dependence on parameter estimates of autoregressive process with Gumbel distributed innovation |
| title_sort | impact of dependence on parameter estimates of autoregressive process with gumbel distributed innovation |
| url | http://psasir.upm.edu.my/id/eprint/74562/1/Impact%20of%20dependence%20on%20parameter%20estimates%20of%20autoregressive%20process%20with%20Gumbel%20distributed%20innovation.pdf |
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