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Model Checking Via Parametric Bootstraps in Time Series Analysis

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  • Ruey S. Tsay

Abstract

This paper uses parametric bootstraps in conjunction with selected functionals such as the spectral density function to derive methods for model checking in time series analysis. The methods proposed emphasize the reproducibilities of the fitted models. They are widely applicable and easy to implement. In particular, they can be used to check special characteristics of the underlying process such as time reversibility and long memory dependence. The paper also addresses the importance of model‐building objectives in model checking. Several examples including a wind speed data set for Ireland are used to illustrate the procedures proposed.

Suggested Citation

  • Ruey S. Tsay, 1992. "Model Checking Via Parametric Bootstraps in Time Series Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 1-15, March.
    • Handle: RePEc:bla:jorssc:v:41:y:1992:i:1:p:1-15
    DOI: 10.2307/2347612
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    Cited by:

    1. E. E. Ioannidis & G. A. Chronis, 2005. "Extreme Spectra of Var Models and Orders of Near‐Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(3), pages 399-421, May.
    2. Grunwald, Gary K. & Hyndman, Rob J., 1998. "Smoothing non-Gaussian time series with autoregressive structure," Computational Statistics & Data Analysis, Elsevier, vol. 28(2), pages 171-191, August.
    3. John P. Miller & Paul Newbold, 1995. "A GENERALIZED VARIANCE RATIO TEST OF ARIMA (p, 1, q) MODEL SPECIFICATION," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(4), pages 403-413, July.
    4. Yongning Wang & Ruey S. Tsay, 2013. "On Diagnostic Checking of Vector ARMA-GARCH Models with Gaussian and Student-t Innovations," Econometrics, MDPI, vol. 1(1), pages 1-31, April.
    5. Ristić Miroslav M. & Weiß Christian H. & Janjić Ana D., 2016. "A Binomial Integer-Valued ARCH Model," The International Journal of Biostatistics, De Gruyter, vol. 12(2), pages 1-21, November.
    6. Christian Weiß, 2015. "A Poisson INAR(1) model with serially dependent innovations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 829-851, October.
    7. Cláudia Santos & Isabel Pereira & Manuel G. Scotto, 2021. "On the theory of periodic multivariate INAR processes," Statistical Papers, Springer, vol. 62(3), pages 1291-1348, June.
    8. Zacharias Psaradakis, 1998. "Bootstrap-based evaluation of markov-switching time series models," Econometric Reviews, Taylor & Francis Journals, vol. 17(3), pages 275-288.
    9. Adriana Bortoluzzo & Pedro Morettin & Clelia Toloi, 2010. "Time-varying autoregressive conditional duration model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(5), pages 847-864.
    10. Bortoluzzo, Adriana B. & Morettin, Pedro A. & Toloi, Clelia M. C., 2008. "Time-Varying Autoregressive Conditional Duration Model," Insper Working Papers wpe_174, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
    11. Vance L. Martin & Andrew R. Tremayne & Robert C. Jung, 2014. "Efficient Method Of Moments Estimators For Integer Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 491-516, November.
    12. Andreea Röthig & Andreas Röthig & Carl Chiarella, 2015. "On Candlestick-based Trading Rules Profitability Analysis via Parametric Bootstraps and Multivariate Pair-Copula based Models," Research Paper Series 362, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. Newbold, Paul & Leybourne, Stephen & Wohar, Mark E., 2001. "Trend-stationarity, difference-stationarity, or neither: further diagnostic tests with an application to U.S. Real GNP, 1875-1993," Journal of Economics and Business, Elsevier, vol. 53(1), pages 85-102.
    14. Jentsch, Carsten & Weiß, Christian, 2017. "Bootstrapping INAR models," Working Papers 17-02, University of Mannheim, Department of Economics.
    15. Christian H. Weiß & Martin H.-J. M. Feld & Naushad Mamode Khan & Yuvraj Sunecher, 2019. "INARMA Modeling of Count Time Series," Stats, MDPI, vol. 2(2), pages 1-37, June.
    16. Nielsen, Henrik Aa. & Madsen, Henrik, 2001. "A generalization of some classical time series tools," Computational Statistics & Data Analysis, Elsevier, vol. 37(1), pages 13-31, July.
    17. Zhang, Michael Yuanjie & Russell, Jeffrey R. & Tsay, Ruey S., 2001. "A nonlinear autoregressive conditional duration model with applications to financial transaction data," Journal of Econometrics, Elsevier, vol. 104(1), pages 179-207, August.
    18. Robert C. Jung & Andrew R. Tremayne, 2020. "Maximum-Likelihood Estimation in a Special Integer Autoregressive Model," Econometrics, MDPI, vol. 8(2), pages 1-15, June.

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