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Bootstrapping the portmanteau tests in weak auto-regressive moving average models

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  • Ke Zhu

Abstract

This paper uses a random weighting (RW) method to bootstrap the critical values for the Ljung-Box/Monti portmanteau tests and weighted Ljung-Box/Monti portmanteau tests in weak ARMA models. Unlike the existing methods, no user-chosen parameter is needed to implement the RW method. As an application, these four tests are used to check the model adequacy in power GARCH models. Simulation evidence indicates that the weighted portmanteau tests have the power advantage over other existing tests. A real example on S&P 500 index illustrates the merits of our testing procedure. As one extension work, the block-wise RW method is also studied.
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  • Ke Zhu, 2016. "Bootstrapping the portmanteau tests in weak auto-regressive moving average models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 463-485, March.
    • Handle: RePEc:bla:jorssb:v:78:y:2016:i:2:p:463-485
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    3. Mengya Liu & Fukan Zhu & Ke Zhu, 2020. "Multi-frequency-band tests for white noise under heteroskedasticity," Papers 2004.09161, arXiv.org.
    4. Li, Dong & Ling, Shiqing & Zhu, Ke, 2016. "ZD-GARCH model: a new way to study heteroscedasticity," MPRA Paper 68621, University Library of Munich, Germany.
    5. Guo, Shaojun & Li, Dong & Li, Muyi, 2019. "Strict stationarity testing and GLAD estimation of double autoregressive models," Journal of Econometrics, Elsevier, vol. 211(2), pages 319-337.
    6. Ding, Jing & Jiang, Lei & Liu, Xiaohui & Peng, Liang, 2023. "Nonparametric tests for market timing ability using daily mutual fund returns," Journal of Economic Dynamics and Control, Elsevier, vol. 150(C).
    7. Peng, Liang & Einmahl, John, 2021. "Improved regression inference using a second overlapping regression model," Other publications TiSEM c529c2b9-0eee-440e-b015-8, Tilburg University, School of Economics and Management.
    8. Feiyu Jiang & Dong Li & Ke Zhu, 2019. "Non-standard inference for augmented double autoregressive models with null volatility coefficients," Papers 1905.01798, arXiv.org.
    9. Ke Zhu, 2018. "Statistical inference for autoregressive models under heteroscedasticity of unknown form," Papers 1804.02348, arXiv.org, revised Aug 2018.
    10. Jiang, Feiyu & Li, Dong & Zhu, Ke, 2020. "Non-standard inference for augmented double autoregressive models with null volatility coefficients," Journal of Econometrics, Elsevier, vol. 215(1), pages 165-183.
    11. Yawen Fan & Xiaohui Liu & Yang Cao & Shaochu Liu, 2024. "Jackknife empirical likelihood based diagnostic checking for Ar(p) models," Computational Statistics, Springer, vol. 39(5), pages 2479-2509, July.
    12. Guo, Shaojun & Li, Dong & Li, Muyi, 2018. "Strict Stationarity Testing and GLAD Estimation of Double Autoregressive Models," IRTG 1792 Discussion Papers 2018-049, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    13. Peng, Liang & Einmahl, John, 2021. "Improved regression inference using a second overlapping regression model," Discussion Paper 2021-029, Tilburg University, Center for Economic Research.
    14. Feiyu Jiang & Dong Li & Ke Zhu, 2019. "Adaptive inference for a semiparametric generalized autoregressive conditional heteroskedasticity model," Papers 1907.04147, arXiv.org, revised Oct 2020.
    15. Li, Dong & Zhang, Xingfa & Zhu, Ke & Ling, Shiqing, 2018. "The ZD-GARCH model: A new way to study heteroscedasticity," Journal of Econometrics, Elsevier, vol. 202(1), pages 1-17.
    16. Ying Liao & Cuixia Li & Lei Jiang & Liang Peng, 2021. "Quantifying Diseconomies Of Scale For Mutual Funds," Annals of Economics and Finance, Society for AEF, vol. 22(1), pages 1-24, May.
    17. Li, Yinhuan & Fung, Tsz Chai & Peng, Liang & Qian, Linyi, 2023. "Diagnostic tests before modeling longitudinal actuarial data," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 310-325.

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    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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