IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v33y2024i3d10.1007_s11749-024-00930-0.html
   My bibliography  Save this article

Local influence analysis in the softplus INGARCH model

Author

Listed:
  • Zhonghao Su

    (Jilin University)

  • Fukang Zhu

    (Jilin University)

  • Shuangzhe Liu

    (University of Canberra)

Abstract

In statistical diagnostics, detecting influential observations is pivotal for assessing model fitting. To address parameter restrictions while maintaining necessary properties, the softplus INGARCH model has emerged as an alternative to the INGARCH model and its variants. This paper delves into statistical diagnostics within the softplus INGARCH model using local influence analysis, establishing a framework encompassing first-order diagnostics, second-order diagnostics and stepwise diagnostics. Additionally, we focus on perturbation schemes, refining conventional approaches and offering modifications. To demonstrate the effectiveness and suitability of our proposed methodology, particularly with the inclusion of stepwise diagnostics, we analyze two simulated datasets and two real-world examples. Compared to traditional methods, our approach adeptly handles potential issues such as the “masking effect” and “smearing effect” without necessitating complex calculations.

Suggested Citation

  • Zhonghao Su & Fukang Zhu & Shuangzhe Liu, 2024. "Local influence analysis in the softplus INGARCH model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(3), pages 951-985, September.
    • Handle: RePEc:spr:testjl:v:33:y:2024:i:3:d:10.1007_s11749-024-00930-0
    DOI: 10.1007/s11749-024-00930-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-024-00930-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11749-024-00930-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Alejandra Tapia & Victor Leiva & Maria del Pilar Diaz & Viviana Giampaoli, 2019. "Influence diagnostics in mixed effects logistic regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 920-942, September.
    2. Aline B. Tsuyuguchi & Gilberto A. Paula & Michelli Barros, 2020. "Analysis of correlated Birnbaum–Saunders data based on estimating equations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 661-681, September.
    3. Riani, Marco & Atkinson, Anthony Curtis & Corbellini, Aldo & Farcomeni, Alessio & Laurini, Fabrizio, 2024. "Information Criteria for Outlier Detection Avoiding Arbitrary Significance Levels," Econometrics and Statistics, Elsevier, vol. 29(C), pages 189-205.
    4. Manuel Galea & Patricia Giménez, 2019. "Local influence diagnostics for the test of mean–variance efficiency and systematic risks in the capital asset pricing model," Statistical Papers, Springer, vol. 60(1), pages 293-312, February.
    5. Prendergast, Luke A. & Smith, Jodie A., 2022. "Influence functions for linear discriminant analysis: Sensitivity analysis and efficient influence diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    6. W.‐Y. Poon & Y. S. Poon, 1999. "Conformal normal curvature and assessment of local influence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 51-61.
    7. Chen, Cathy W.S. & Lee, Sangyeol, 2016. "Generalized Poisson autoregressive models for time series of counts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 51-67.
    8. Lei Shi & Md. Mostafizur Rahman & Wen Gan & Jianhua Zhao, 2015. "Stepwise local influence in generalized autoregressive conditional heteroskedasticity models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 428-444, February.
    9. Xibin Zhang & Maxwell L. King, 2005. "Influence Diagnostics in Generalized Autoregressive Conditional Heteroscedasticity Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 118-129, January.
    10. Fukang Zhu & Shuangzhe Liu & Lei Shi, 2016. "Local influence analysis for Poisson autoregression with an application to stock transaction data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(1), pages 4-25, February.
    11. Lindsay R. Berry & Mike West, 2020. "Bayesian Forecasting of Many Count-Valued Time Series," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(4), pages 872-887, October.
    12. Fokianos, Konstantinos & Fried, Roland & Kharin, Yuriy & Voloshko, Valeriy, 2022. "Statistical analysis of multivariate discrete-valued time series," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    13. E. Gonçalves & N. Mendes-Lopes & F. Silva, 2015. "Infinitely Divisible Distributions in Integer-Valued Garch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 503-527, July.
    14. Reiko Aoki & Juan P. M. Bustamante & Gilberto A. Paula, 2022. "Local influence diagnostics with forward search in regression analysis," Statistical Papers, Springer, vol. 63(5), pages 1477-1497, October.
    15. Rodrigo B. Silva & Wagner Barreto‐Souza, 2019. "Flexible and Robust Mixed Poisson INGARCH Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(5), pages 788-814, September.
    16. Shi, Lei & Huang, Mei, 2011. "Stepwise local influence analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 973-982, February.
    17. Yan Cui & Fukang Zhu, 2018. "A new bivariate integer-valued GARCH model allowing for negative cross-correlation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 428-452, June.
    18. Liu, Shuangzhe & Leiva, Víctor & Zhuang, Dan & Ma, Tiefeng & Figueroa-Zúñiga, Jorge I., 2022. "Matrix differential calculus with applications in the multivariate linear model and its diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    19. Richard A. Davis & Konstantinos Fokianos & Scott H. Holan & Harry Joe & James Livsey & Robert Lund & Vladas Pipiras & Nalini Ravishanker, 2021. "Count Time Series: A Methodological Review," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1533-1547, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Fukang Zhu & Shuangzhe Liu & Lei Shi, 2016. "Local influence analysis for Poisson autoregression with an application to stock transaction data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 70(1), pages 4-25, February.
    2. Yonghui Liu & Ruochen Sang & Shuangzhe Liu, 2017. "Diagnostic analysis for a vector autoregressive model under Student-super-′s t-distributions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 71(2), pages 86-114, May.
    3. Xiaowen Dai & Libin Jin & Maozai Tian & Lei Shi, 2019. "Bayesian Local Influence for Spatial Autoregressive Models with Heteroscedasticity," Statistical Papers, Springer, vol. 60(5), pages 1423-1446, October.
    4. Xiaowen Dai & Libin Jin & Lei Shi & Cuiping Yang & Shuangzhe Liu, 2016. "Local influence analysis in general spatial models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(3), pages 313-331, July.
    5. Luiza S. C. Piancastelli & Wagner Barreto‐Souza & Hernando Ombao, 2023. "Flexible bivariate INGARCH process with a broad range of contemporaneous correlation," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(2), pages 206-222, March.
    6. Fokianos, Konstantinos, 2024. "Multivariate Count Time Series Modelling," Econometrics and Statistics, Elsevier, vol. 31(C), pages 100-116.
    7. Lei Shi & Md. Mostafizur Rahman & Wen Gan & Jianhua Zhao, 2015. "Stepwise local influence in generalized autoregressive conditional heteroskedasticity models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 428-444, February.
    8. Fukang Zhu & Lei Shi & Shuangzhe Liu, 2015. "Influence diagnostics in log-linear integer-valued GARCH models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(3), pages 311-335, July.
    9. Yonghui Liu & Guohua Mao & Víctor Leiva & Shuangzhe Liu & Alejandra Tapia, 2020. "Diagnostic Analytics for an Autoregressive Model under the Skew-Normal Distribution," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    10. Fokianos, Konstantinos & Fried, Roland & Kharin, Yuriy & Voloshko, Valeriy, 2022. "Statistical analysis of multivariate discrete-valued time series," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    11. Chen, Cathy W.S. & Chen, Chun-Shu & Hsiung, Mo-Hua, 2023. "Bayesian modeling of spatial integer-valued time series," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
    12. Shi, Lei & Lu, Jun & Zhao, Jianhua & Chen, Gemai, 2016. "Case deletion diagnostics for GMM estimation," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 176-191.
    13. Jun Lu & Wen Gan & Lei Shi, 2022. "Local influence analysis for GMM estimation," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(1), pages 1-23, March.
    14. Yuhyeong Jang & Raanju R. Sundararajan & Wagner Barreto-Souza & Elizabeth Wheaton-Paramo, 2024. "Determining economic factors for sex trafficking in the United States using count time series regression," Empirical Economics, Springer, vol. 67(1), pages 337-354, July.
    15. Manuel Galea & Patricia Giménez, 2019. "Local influence diagnostics for the test of mean–variance efficiency and systematic risks in the capital asset pricing model," Statistical Papers, Springer, vol. 60(1), pages 293-312, February.
    16. Yang, Kai & Yu, Xinyang & Zhang, Qingqing & Dong, Xiaogang, 2022. "On MCMC sampling in self-exciting integer-valued threshold time series models," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    17. Randal Douc & François Roueff & Tepmony Sim, 2021. "Necessary and sufficient conditions for the identifiability of observation‐driven models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(2), pages 140-160, March.
    18. Francisco J. A. Cysneiros & Víctor Leiva & Shuangzhe Liu & Carolina Marchant & Paulo Scalco, 2019. "A Cobb–Douglas type model with stochastic restrictions: formulation, local influence diagnostics and data analytics in economics," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(4), pages 1693-1719, July.
    19. Qi Li & Fukang Zhu, 2020. "Mean targeting estimator for the integer-valued GARCH(1, 1) model," Statistical Papers, Springer, vol. 61(2), pages 659-679, April.
    20. Ovielt Baltodano Lopez & Federico Bassetti & Giulia Carallo & Roberto Casarin, 2022. "First-order integer-valued autoregressive processes with Generalized Katz innovations," Papers 2202.02029, arXiv.org, revised Dec 2024.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:testjl:v:33:y:2024:i:3:d:10.1007_s11749-024-00930-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.