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A bootstrapped spectral test for adequacy in weak ARMA models

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  • Zhu, Ke
  • Li, Wai-Keung

Abstract

This paper proposes a Cramer-von Mises (CM) test statistic to check the adequacy of weak ARMA models. Without posing a martingale difference assumption on the error terms, the asymptotic null distribution of the CM test is obtained by using the Hillbert space approach. Moreover, this CM test is consistent, and has nontrivial power against the local alternative of order $n^{-1/2}$. Due to the unknown dependence of error terms and the estimation effects, a new block-wise random weighting method is constructed to bootstrap the critical values of the test statistic. The new method is easy to implement and its validity is justified. The theory is illustrated by a small simulation study and an application to S\&P 500 stock index.

Suggested Citation

  • Zhu, Ke & Li, Wai-Keung, 2013. "A bootstrapped spectral test for adequacy in weak ARMA models," MPRA Paper 51224, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:51224
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    Cited by:

    1. Li, Linyuan & Duchesne, Pierre & Liou, Chu Pheuil, 2021. "On diagnostic checking in ARMA models with conditionally heteroscedastic martingale difference using wavelet methods," Econometrics and Statistics, Elsevier, vol. 19(C), pages 169-187.
    2. Ke Zhu & Shiqing Ling, 2015. "LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 784-794, June.
    3. Zhang, Xianyang, 2016. "White noise testing and model diagnostic checking for functional time series," Journal of Econometrics, Elsevier, vol. 194(1), pages 76-95.
    4. Ke Zhu, 2018. "Statistical inference for autoregressive models under heteroscedasticity of unknown form," Papers 1804.02348, arXiv.org, revised Aug 2018.
    5. Hill, Jonathan B. & Motegi, Kaiji, 2019. "Testing the white noise hypothesis of stock returns," Economic Modelling, Elsevier, vol. 76(C), pages 231-242.
    6. Yacouba Boubacar Maïnassara & Youssef Esstafa & Bruno Saussereau, 2021. "Estimating FARIMA models with uncorrelated but non-independent error terms," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 549-608, October.
    7. Li, Muyi & Zhang, Yanfen, 2022. "Bootstrapping multivariate portmanteau tests for vector autoregressive models with weak assumptions on errors," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    8. Wang, Xuqin & Li, Muyi, 2023. "Bootstrapping the transformed goodness-of-fit test on heavy-tailed GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    9. 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.

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    More about this item

    Keywords

    Block-wise random weighting method; Diagnostic checking; Least squares estimation; Spectral test; Weak ARMA models; Wild bootstrap.;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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