Zero-Inflated Rayleigh Dynamic Model for Non-Negative Signals
This study proposes a zero-inflated Rayleigh seasonal autoregressive moving average model with exogenous regressors (iRSARMAX) to model and forecast non-negative time series, accommodating the presence of zero values. The proposed iRSARMAX models the conditional mean of the continuous part of the mi...
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IEEE
2024-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10792885/ |
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| author | Aline Armanini Stefanan Bruna G. Palm Fabio M. Bayer |
| author_facet | Aline Armanini Stefanan Bruna G. Palm Fabio M. Bayer |
| author_sort | Aline Armanini Stefanan |
| collection | DOAJ |
| description | This study proposes a zero-inflated Rayleigh seasonal autoregressive moving average model with exogenous regressors (iRSARMAX) to model and forecast non-negative time series, accommodating the presence of zero values. The proposed iRSARMAX models the conditional mean of the continuous part of the mixture distribution by using a dynamic structure that considers stochastic seasonality, autoregressive and moving average terms, exogenous regressors, and a link function. It also models the mixture parameters related to the inflated (zero) values with a parsimonious dynamic structure. Furthermore, the analytical score vector was deduced and considered in the conditional maximum likelihood estimation of the introduced model parameters. The analytical Fisher information matrix was obtained and used for hypothesis testing and interval inferences for the parameters of the proposed model. Randomized quantile residuals were considered, and goodness-of-fit tests were implemented to validate the model. An extensive simulation study was performed to evaluate the performance of conditional likelihood inference over the model parameters for finite sample sizes. The proposed model excelled compared to the traditional seasonal autoregressive and moving average model and the Holt-Winters filtering in forecasting influent flow. In addition, it outperformed competitors in predicting synthetic aperture radar (SAR) image data. |
| format | Article |
| id | doaj-art-21b7add890fc44d8ad4edb5a3b57afb6 |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-21b7add890fc44d8ad4edb5a3b57afb62024-12-18T00:01:40ZengIEEEIEEE Access2169-35362024-01-011218709918711110.1109/ACCESS.2024.351564710792885Zero-Inflated Rayleigh Dynamic Model for Non-Negative SignalsAline Armanini Stefanan0https://orcid.org/0000-0002-3994-2586Bruna G. Palm1https://orcid.org/0000-0003-0423-9927Fabio M. Bayer2https://orcid.org/0000-0002-1464-0805Postgraduate Program in Industrial Engineering, Federal University of Santa Maria, Santa Maria, State of Rio Grande do Sul, BrazilDepartment of Mathematics and Natural Sciences, Blekinge Institute of Technology, Karlskrona, Blekinge, SwedenDepartment of Statistics, Federal University of Santa Maria, Santa Maria, State of Rio Grande do Sul, BrazilThis study proposes a zero-inflated Rayleigh seasonal autoregressive moving average model with exogenous regressors (iRSARMAX) to model and forecast non-negative time series, accommodating the presence of zero values. The proposed iRSARMAX models the conditional mean of the continuous part of the mixture distribution by using a dynamic structure that considers stochastic seasonality, autoregressive and moving average terms, exogenous regressors, and a link function. It also models the mixture parameters related to the inflated (zero) values with a parsimonious dynamic structure. Furthermore, the analytical score vector was deduced and considered in the conditional maximum likelihood estimation of the introduced model parameters. The analytical Fisher information matrix was obtained and used for hypothesis testing and interval inferences for the parameters of the proposed model. Randomized quantile residuals were considered, and goodness-of-fit tests were implemented to validate the model. An extensive simulation study was performed to evaluate the performance of conditional likelihood inference over the model parameters for finite sample sizes. The proposed model excelled compared to the traditional seasonal autoregressive and moving average model and the Holt-Winters filtering in forecasting influent flow. In addition, it outperformed competitors in predicting synthetic aperture radar (SAR) image data.https://ieeexplore.ieee.org/document/10792885/ARMA modelinflated Rayleigh distributioniRSARMAX modeltime series |
| spellingShingle | Aline Armanini Stefanan Bruna G. Palm Fabio M. Bayer Zero-Inflated Rayleigh Dynamic Model for Non-Negative Signals IEEE Access ARMA model inflated Rayleigh distribution iRSARMAX model time series |
| title | Zero-Inflated Rayleigh Dynamic Model for Non-Negative Signals |
| title_full | Zero-Inflated Rayleigh Dynamic Model for Non-Negative Signals |
| title_fullStr | Zero-Inflated Rayleigh Dynamic Model for Non-Negative Signals |
| title_full_unstemmed | Zero-Inflated Rayleigh Dynamic Model for Non-Negative Signals |
| title_short | Zero-Inflated Rayleigh Dynamic Model for Non-Negative Signals |
| title_sort | zero inflated rayleigh dynamic model for non negative signals |
| topic | ARMA model inflated Rayleigh distribution iRSARMAX model time series |
| url | https://ieeexplore.ieee.org/document/10792885/ |
| work_keys_str_mv | AT alinearmaninistefanan zeroinflatedrayleighdynamicmodelfornonnegativesignals AT brunagpalm zeroinflatedrayleighdynamicmodelfornonnegativesignals AT fabiombayer zeroinflatedrayleighdynamicmodelfornonnegativesignals |