Proper ARMA Modeling and Forecasting in the Generalized Segre’s Quaternions Domain
The analysis of time series in 4D commutative hypercomplex algebras is introduced. Firstly, generalized Segre’s quaternion (GSQ) random variables and signals are studied. Then, two concepts of properness are suggested and statistical tests to check if a GSQ random vector is proper or not are propose...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/7/1083 |
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| author | Jesús Navarro-Moreno Rosa M. Fernández-Alcalá Juan C. Ruiz-Molina |
| author_facet | Jesús Navarro-Moreno Rosa M. Fernández-Alcalá Juan C. Ruiz-Molina |
| author_sort | Jesús Navarro-Moreno |
| collection | DOAJ |
| description | The analysis of time series in 4D commutative hypercomplex algebras is introduced. Firstly, generalized Segre’s quaternion (GSQ) random variables and signals are studied. Then, two concepts of properness are suggested and statistical tests to check if a GSQ random vector is proper or not are proposed. Further, a method to determine in which specific hypercomplex algebra is most likely to achieve, if possible, the properness properties is given. Next, both the linear estimation and prediction problems are studied in the GSQ domain. Finally, ARMA modeling and forecasting for proper GSQ time series are tackled. Experimental results show the superiority of the proposed approach over its counterpart in the Hamilton quaternion domain. |
| first_indexed | 2024-03-09T11:39:15Z |
| format | Article |
| id | doaj.art-7556065b29f1450496b50dc9e606dc0e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:39:15Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7556065b29f1450496b50dc9e606dc0e2023-11-30T23:36:55ZengMDPI AGMathematics2227-73902022-03-01107108310.3390/math10071083Proper ARMA Modeling and Forecasting in the Generalized Segre’s Quaternions DomainJesús Navarro-Moreno0Rosa M. Fernández-Alcalá1Juan C. Ruiz-Molina2Department of Statistics and Operations Research, University of Jaén, Paraje Las Lagunillas, 23071 Jaén, SpainDepartment of Statistics and Operations Research, University of Jaén, Paraje Las Lagunillas, 23071 Jaén, SpainDepartment of Statistics and Operations Research, University of Jaén, Paraje Las Lagunillas, 23071 Jaén, SpainThe analysis of time series in 4D commutative hypercomplex algebras is introduced. Firstly, generalized Segre’s quaternion (GSQ) random variables and signals are studied. Then, two concepts of properness are suggested and statistical tests to check if a GSQ random vector is proper or not are proposed. Further, a method to determine in which specific hypercomplex algebra is most likely to achieve, if possible, the properness properties is given. Next, both the linear estimation and prediction problems are studied in the GSQ domain. Finally, ARMA modeling and forecasting for proper GSQ time series are tackled. Experimental results show the superiority of the proposed approach over its counterpart in the Hamilton quaternion domain.https://www.mdpi.com/2227-7390/10/7/1083ARMA models<i>E</i><sub><i>α</i><sub>0</sub></sub>-propernessgeneralized Segre’s quaternions<i>H</i><sub><i>α</i><sub>0</sub></sub>-propernesspredictionproper signal processing |
| spellingShingle | Jesús Navarro-Moreno Rosa M. Fernández-Alcalá Juan C. Ruiz-Molina Proper ARMA Modeling and Forecasting in the Generalized Segre’s Quaternions Domain Mathematics ARMA models <i>E</i><sub><i>α</i><sub>0</sub></sub>-properness generalized Segre’s quaternions <i>H</i><sub><i>α</i><sub>0</sub></sub>-properness prediction proper signal processing |
| title | Proper ARMA Modeling and Forecasting in the Generalized Segre’s Quaternions Domain |
| title_full | Proper ARMA Modeling and Forecasting in the Generalized Segre’s Quaternions Domain |
| title_fullStr | Proper ARMA Modeling and Forecasting in the Generalized Segre’s Quaternions Domain |
| title_full_unstemmed | Proper ARMA Modeling and Forecasting in the Generalized Segre’s Quaternions Domain |
| title_short | Proper ARMA Modeling and Forecasting in the Generalized Segre’s Quaternions Domain |
| title_sort | proper arma modeling and forecasting in the generalized segre s quaternions domain |
| topic | ARMA models <i>E</i><sub><i>α</i><sub>0</sub></sub>-properness generalized Segre’s quaternions <i>H</i><sub><i>α</i><sub>0</sub></sub>-properness prediction proper signal processing |
| url | https://www.mdpi.com/2227-7390/10/7/1083 |
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