A Change-point Detection Test in a Class of INAR(1) Processes Using the Empirical Likelihood Method

Nakhaeezadeh, Zohreh; Jomhoori, Sarah; Yousefzadeh, Fatemeh

doi:10.61186/jss.19.2.01

[Home ] [Archive]

[ فارسی ]

مجله علوم آماری – نشریه علمی پژوهشی انجمن آمار ایران

Main Menu

Home

Journal Information

Articles archive

For Authors

For Reviewers

Registration

Ethics Considerations

Contact us

Site Facilities

Search in website

Receive site information

Indexing and Abstracting

Social Media

Licenses

This Journal is licensed under a Creative Commons Attribution NonCommercial 4.0
International License
(CC BY-NC 4.0).

Similarity Check Systems

Back to the articles list

Back to browse issues page

A Change-point Detection Test in a Class of INAR(1) Processes Using the Empirical Likelihood Method

Zohreh Nakhaeezadeh

, Sarah Jomhoori ^*

, Fatemeh Yousefzadeh

Abstract: (14 Views)

Integer-valued time series models play an essential role in the analysis of dependent count data. One of the main challenges in these models is to detect structural changes over time. These changes may be caused by sudden interventions such as policy changes, pandemics, or system failures. In this paper, the empirical likelihood method is used to detect structural changes in a class of INAR(1) processes. This method is a tool for early warning of structural changes in these processes. Using simulation, the empirical sizes and powers of the test are calculated for different sample sizes, and the test's performance is investigated. Finally, the practical efficiency of the test is investigated by identifying the change point in two real datasets: the number of robberies and the number of COVID-19 deaths.

Keywords: Change point‎, ‎Count time series‎, ‎Empirical likelihood‎, ‎INAR model

Full-Text [PDF 6702 kb] (13 Downloads)

Type of Study: Applied | Subject: Statistical Inference
Received: 2025/06/27 | Accepted: 2025/11/18

References

1. شیراوژن، م.، محمدپور، م. ‎(1399)‎، مدل خودبازگشتی صحیح مقدار مرتبه اول براساس عملگر نازک دوجمله‌ای منفی با نوفه‌های وابسته، مجله علوم آماری، 1‎، 215-232.

2. Al-Osh, M. A. and Alzaid, A. A. (1987), First-Order Integer-Valued Autoregressive (INAR(1)) Process. Journal of Time Series Analysis, 8, 261-275. [DOI:10.1111/j.1467-9892.1987.tb00438.x]

3. Baragona, R., Battaglia, F. and Cucina D. (2013), Empirical Likelihood for Break Detection in Time Series. Electron Journal of Statistics, 7, 3089-3123. [DOI:10.1214/13-EJS873]

4. Ding, X. and Wang, D. (2016), Empirical Likelihood Inference for INAR(1) Model with Explanatory Variables. Journal of Korean Statistical Society, 45, 623-632. [DOI:10.1016/j.jkss.2016.05.004]

5. Gamage, R. D. P. and Ning, W. (2021) Empirical Likelihood for Change Point Detection in Autoregressive Models. Journal of Korean Statistical Society. 50, 69-97. [DOI:10.1007/s42952-020-00061-w]

6. Kang, J., Lee, S. (2009), Parameter Change Test for Random Coefficient Integer-Valued Autoregressive Processes with Application to Polio Data Analysis. Journal of Time Series Analysis, 30, 239-258. [DOI:10.1111/j.1467-9892.2009.00608.x]

7. Owen A. B. (1990), Empirical Likelihood Ratio Confidence Regions. Annals of Statistics, 18, 90-120. [DOI:10.1214/aos/1176347494]

8. Piyadi Gamage, R. D., and Ning, W. (2021), Empirical Likelihood for Change Point Detection in Autoregressive Models. Journal of the Korean Statistical Society, 50(1), 69-97. [DOI:10.1007/s42952-020-00061-w]

9. Qin, J. and Lawless, J. (1994), Empirical Likelihood and General Estimating Equations. The Annals of Statistics, 22, 300-325. [DOI:10.1214/aos/1176325370]

10. Ristić, M. M., Bakouch, H. S. and Nastić, A. S. (2009), A New Geometric First Order Integer-Valued Autoregressive (NGINAR(1)) Process. Journal of Statistical Planning and Inference, 139, 2218-2226. [DOI:10.1016/j.jspi.2008.10.007]

11. Shirozhan, M., Mohammadpour, M. (2019), An INAR(1) Model Based on Negative Binomial Thinning Operator with Serially Dependent Noise. Journal of Statistical Sciences, 1, 215-232. [DOI:10.29252/jss.14.1.217]

12. Steutel, F. and van Harn, K. (1979), Discrete Analogues of Self Decomposability and Stability. The Annals of Probability, 7, 893-899. [DOI:10.1214/aop/1176994950]

13. White, H. (2001), Asymptotic Theory for Econometricians. London: Academic Press.

14. Weiß, C. H. (2008), Thinning Operations for Modeling Time Series of Counts: a Survey. ASTA Advances in Statistical Analysis, 92, 319-343. [DOI:10.1007/s10182-008-0072-3]

15. Weiß, C. H. and Kim, H. Y. (2014), Diagnosing and Modelling Extra-Binomial Variation for Time-Dependent Counts. Applied Stochastic Models in Business and Industry, 30, 588-608. [DOI:10.1002/asmb.2005]

16. Yu, K., Wang, H. and Weiß, C. H. (2023), An Empirical-Likelihood Based Structural-Change Test for INAR Processes, Journal of Statistical Computation and Simulation, 93, 442-458. [DOI:10.1080/00949655.2022.2109635]

17. Yu, M., Wang, D. and Yang, K. (2019), A Class of Observation-Driven Random Coefficient INAR (1) Processes Based on Negative Binomial Thinning. Journal of the Korean Statistical Society, 48, 248-264. [DOI:10.1016/j.jkss.2018.11.004]

18. Zhang, H., Wang, D., and Zhu, F. (2011), Empirical Likelihood Inference for Random Coefficient INAR(p) Process. Journal of Time Series Analysis. 32, 195-203. [DOI:10.1111/j.1467-9892.2010.00691.x]

19. Zhang, H., Wang, D. and Zhu, F. (2012), Generalized RCINAR(1) Process with Signed Thinning Operator. Communications in Statistics: Theory and Methods, 41, 1750- 1770. [DOI:10.1080/03610926.2010.551452]

20. Zhu, F., Liu, M., Ling, S. and Cai, Z. (2022), Testing for Structural Change of Predictive Regression Model to Threshold Predictive Regression Model. Journal of Business and Economic Statistics, 41, 228-240. [DOI:10.1080/07350015.2021.2008406]

Send email to the article author

Add your comments about this article