Fisher’s <i>z</i> Distribution-Based Mixture Autoregressive Model
We generalize the Gaussian Mixture Autoregressive (GMAR) model to the Fisher’s <i>z</i> Mixture Autoregressive (ZMAR) model for modeling nonlinear time series. The model consists of a mixture of <i>K</i>-component Fisher’s <i>z</i> autoregressive models with the m...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Econometrics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2225-1146/9/3/27 |
| _version_ | 1827688534838870016 |
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| author | Arifatus Solikhah Heri Kuswanto Nur Iriawan Kartika Fithriasari |
| author_facet | Arifatus Solikhah Heri Kuswanto Nur Iriawan Kartika Fithriasari |
| author_sort | Arifatus Solikhah |
| collection | DOAJ |
| description | We generalize the Gaussian Mixture Autoregressive (GMAR) model to the Fisher’s <i>z</i> Mixture Autoregressive (ZMAR) model for modeling nonlinear time series. The model consists of a mixture of <i>K</i>-component Fisher’s <i>z</i> autoregressive models with the mixing proportions changing over time. This model can capture time series with both heteroskedasticity and multimodal conditional distribution, using Fisher’s <i>z</i> distribution as an innovation in the MAR model. The ZMAR model is classified as nonlinearity in the level (or mode) model because the mode of the Fisher’s <i>z</i> distribution is stable in its location parameter, whether symmetric or asymmetric. Using the Markov Chain Monte Carlo (MCMC) algorithm, e.g., the No-U-Turn Sampler (NUTS), we conducted a simulation study to investigate the model performance compared to the GMAR model and Student <i>t</i> Mixture Autoregressive (TMAR) model. The models are applied to the daily IBM stock prices and the monthly Brent crude oil prices. The results show that the proposed model outperforms the existing ones, as indicated by the Pareto-Smoothed Important Sampling Leave-One-Out cross-validation (PSIS-LOO) minimum criterion. |
| first_indexed | 2024-03-10T09:58:08Z |
| format | Article |
| id | doaj.art-d5683b763d4340ce9a8298760e887e89 |
| institution | Directory Open Access Journal |
| issn | 2225-1146 |
| language | English |
| last_indexed | 2024-03-10T09:58:08Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Econometrics |
| spelling | doaj.art-d5683b763d4340ce9a8298760e887e892023-11-22T02:12:36ZengMDPI AGEconometrics2225-11462021-06-01932710.3390/econometrics9030027Fisher’s <i>z</i> Distribution-Based Mixture Autoregressive ModelArifatus Solikhah0Heri Kuswanto1Nur Iriawan2Kartika Fithriasari3Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, IndonesiaDepartment of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, IndonesiaDepartment of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, IndonesiaDepartment of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, IndonesiaWe generalize the Gaussian Mixture Autoregressive (GMAR) model to the Fisher’s <i>z</i> Mixture Autoregressive (ZMAR) model for modeling nonlinear time series. The model consists of a mixture of <i>K</i>-component Fisher’s <i>z</i> autoregressive models with the mixing proportions changing over time. This model can capture time series with both heteroskedasticity and multimodal conditional distribution, using Fisher’s <i>z</i> distribution as an innovation in the MAR model. The ZMAR model is classified as nonlinearity in the level (or mode) model because the mode of the Fisher’s <i>z</i> distribution is stable in its location parameter, whether symmetric or asymmetric. Using the Markov Chain Monte Carlo (MCMC) algorithm, e.g., the No-U-Turn Sampler (NUTS), we conducted a simulation study to investigate the model performance compared to the GMAR model and Student <i>t</i> Mixture Autoregressive (TMAR) model. The models are applied to the daily IBM stock prices and the monthly Brent crude oil prices. The results show that the proposed model outperforms the existing ones, as indicated by the Pareto-Smoothed Important Sampling Leave-One-Out cross-validation (PSIS-LOO) minimum criterion.https://www.mdpi.com/2225-1146/9/3/27Fisher’s <i>z</i> distributionmixture autoregressive modelthe IBM stock pricesthe Brent crude oil pricesBayesian analysisno-U-turn sampler |
| spellingShingle | Arifatus Solikhah Heri Kuswanto Nur Iriawan Kartika Fithriasari Fisher’s <i>z</i> Distribution-Based Mixture Autoregressive Model Econometrics Fisher’s <i>z</i> distribution mixture autoregressive model the IBM stock prices the Brent crude oil prices Bayesian analysis no-U-turn sampler |
| title | Fisher’s <i>z</i> Distribution-Based Mixture Autoregressive Model |
| title_full | Fisher’s <i>z</i> Distribution-Based Mixture Autoregressive Model |
| title_fullStr | Fisher’s <i>z</i> Distribution-Based Mixture Autoregressive Model |
| title_full_unstemmed | Fisher’s <i>z</i> Distribution-Based Mixture Autoregressive Model |
| title_short | Fisher’s <i>z</i> Distribution-Based Mixture Autoregressive Model |
| title_sort | fisher s i z i distribution based mixture autoregressive model |
| topic | Fisher’s <i>z</i> distribution mixture autoregressive model the IBM stock prices the Brent crude oil prices Bayesian analysis no-U-turn sampler |
| url | https://www.mdpi.com/2225-1146/9/3/27 |
| work_keys_str_mv | AT arifatussolikhah fishersizidistributionbasedmixtureautoregressivemodel AT herikuswanto fishersizidistributionbasedmixtureautoregressivemodel AT nuririawan fishersizidistributionbasedmixtureautoregressivemodel AT kartikafithriasari fishersizidistributionbasedmixtureautoregressivemodel |