Article
| Title: | Modeling a flexible uni/bimodal $\mathbb {Z}$-valued time series with discrete double Lindley innovations: Forecasting via hybrid and statistical approaches (English) |
| Author: | Bakouch, Hassan S. |
| Author: | Gabr, Mahmoud Mohamed |
| Author: | El-Hadidy, Shimaa M. |
| Language: | English |
| Journal: | Applications of Mathematics |
| ISSN: | 0862-7940 (print) |
| ISSN: | 1572-9109 (online) |
| Volume: | 71 |
| Issue: | 5 |
| Year: | 2026 |
| Pages: | 711-741 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | The motivation for implementing this model arises from the need to analyze dependent count data that can take both positive and negative values, exhibit fluctuations around a zero mean, and demonstrate unimodal-bimodal aspects. To capture these features commonly observed in real-world applications, we propose a first-order integer-valued autoregressive process, INAR(1), with discrete double Lindley innovations. The model is constructed using a signed thinning mechanism, referred to as the relative binomial thinning operator, which extends the classical binomial thinning operator. The proposed model is appropriate for $\mathbb {Z}$-valued time series with both positive and negative dependence. The main statistical properties of the process are derived. Parameter estimation is addressed using modified conditional least squares, Yule-Walker, and conditional maximum likelihood methods, whose performance is evaluated through simulation studies. The practical relevance of the model is demonstrated using data from the Saudi stock market. Model adequacy is assessed via standardized residuals and the cumulative periodogram, and predictive performance is evaluated using a hybrid framework combining Support Vector Regression (SVR) with the proposed model, in comparison with bootstrap and classical approaches. (English) |
| Keyword: | $\mathbb {Z}$-valued time series |
| Keyword: | signed thinning operator |
| Keyword: | statistical distribution on $\mathbb {Z}$ |
| Keyword: | simulation |
| Keyword: | SVR-RBINAR-DDL(1) |
| Keyword: | standardized Pearson residual |
| Keyword: | bootstrap |
| Keyword: | forecasting |
| MSC: | 60G10 |
| MSC: | 62M10 |
| MSC: | 62M15 |
| MSC: | 62M20 |
| MSC: | 68T05 |
| DOI: | 10.21136/AM.2026.0070-26 |
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| Date available: | 2026-10-12T13:00:07Z |
| Last updated: | 2026-10-19 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153800 |
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