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Stepwise local influence in generalized autoregressive conditional heteroskedasticity models

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Listed:
  • Lei Shi
  • Md. Mostafizur Rahman
  • Wen Gan
  • Jianhua Zhao

Abstract

Detection of outliers or influential observations is an important work in statistical modeling, especially for the correlated time series data. In this paper we propose a new procedure to detect patch of influential observations in the generalized autoregressive conditional heteroskedasticity (GARCH) model. Firstly we compare the performance of innovative perturbation scheme, additive perturbation scheme and data perturbation scheme in local influence analysis. We find that the innovative perturbation scheme give better result than other two schemes although this perturbation scheme may suffer from masking effects. Then we use the stepwise local influence method under innovative perturbation scheme to detect patch of influential observations and uncover the masking effects. The simulated studies show that the new technique can successfully detect a patch of influential observations or outliers under innovative perturbation scheme. The analysis based on simulation studies and two real data sets show that the stepwise local influence method under innovative perturbation scheme is efficient for detecting multiple influential observations and dealing with masking effects in the GARCH model.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:2:p:428-444
    DOI: 10.1080/02664763.2014.957661
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    References listed on IDEAS

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    Cited by:

    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. 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.
    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. 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.

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