Two-Threshold-Variable Integer-Valued Autoregressive Model
In the past, most threshold models considered a single threshold variable. However, for some practical applications, models with two threshold variables may be needed. In this paper, we propose a two-threshold-variable integer-valued autoregressive model based on the binomial thinning operator and d...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/16/3586 |
| _version_ | 1797583976672526336 |
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| author | Jiayue Zhang Fukang Zhu Huaping Chen |
| author_facet | Jiayue Zhang Fukang Zhu Huaping Chen |
| author_sort | Jiayue Zhang |
| collection | DOAJ |
| description | In the past, most threshold models considered a single threshold variable. However, for some practical applications, models with two threshold variables may be needed. In this paper, we propose a two-threshold-variable integer-valued autoregressive model based on the binomial thinning operator and discuss some of its basic properties, including the mean, variance, strict stationarity, and ergodicity. We consider the conditional least squares (CLS) estimation and discuss the asymptotic normality of the CLS estimator under the known and unknown threshold values. The performances of the CLS estimator are compared via simulation studies. In addition, two real data sets are considered to underline the superior performance of the proposed model. |
| first_indexed | 2024-03-10T23:45:49Z |
| format | Article |
| id | doaj.art-a347a367d2e54cbebb9a3acaaae33808 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T23:45:49Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a347a367d2e54cbebb9a3acaaae338082023-11-19T02:04:11ZengMDPI AGMathematics2227-73902023-08-011116358610.3390/math11163586Two-Threshold-Variable Integer-Valued Autoregressive ModelJiayue Zhang0Fukang Zhu1Huaping Chen2School of Mathematics, Jilin University, Changchun 130012, ChinaSchool of Mathematics, Jilin University, Changchun 130012, ChinaSchool of Mathematics and Statistics, Henan University, Kaifeng 475004, ChinaIn the past, most threshold models considered a single threshold variable. However, for some practical applications, models with two threshold variables may be needed. In this paper, we propose a two-threshold-variable integer-valued autoregressive model based on the binomial thinning operator and discuss some of its basic properties, including the mean, variance, strict stationarity, and ergodicity. We consider the conditional least squares (CLS) estimation and discuss the asymptotic normality of the CLS estimator under the known and unknown threshold values. The performances of the CLS estimator are compared via simulation studies. In addition, two real data sets are considered to underline the superior performance of the proposed model.https://www.mdpi.com/2227-7390/11/16/3586two-threshold-variabletime series of countsinteger-valued autoregressionconditional least squares estimate |
| spellingShingle | Jiayue Zhang Fukang Zhu Huaping Chen Two-Threshold-Variable Integer-Valued Autoregressive Model Mathematics two-threshold-variable time series of counts integer-valued autoregression conditional least squares estimate |
| title | Two-Threshold-Variable Integer-Valued Autoregressive Model |
| title_full | Two-Threshold-Variable Integer-Valued Autoregressive Model |
| title_fullStr | Two-Threshold-Variable Integer-Valued Autoregressive Model |
| title_full_unstemmed | Two-Threshold-Variable Integer-Valued Autoregressive Model |
| title_short | Two-Threshold-Variable Integer-Valued Autoregressive Model |
| title_sort | two threshold variable integer valued autoregressive model |
| topic | two-threshold-variable time series of counts integer-valued autoregression conditional least squares estimate |
| url | https://www.mdpi.com/2227-7390/11/16/3586 |
| work_keys_str_mv | AT jiayuezhang twothresholdvariableintegervaluedautoregressivemodel AT fukangzhu twothresholdvariableintegervaluedautoregressivemodel AT huapingchen twothresholdvariableintegervaluedautoregressivemodel |