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Diagnostics for Time Series Analysis

Author

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  • Richard Gerlach
  • Chris Carter
  • Robert Kohn

Abstract

Test statistics are proposed to determine the goodness of fit of a time series model. The test statistics are based on a sequence of random variables that are independent and standard normal if the model is correct. The paper shows how to compute this sequence of random variables efficiently using a combination of Markov chain Monte Carlo and importance sampling. The power of the statistics to detect outliers and level shifts is studied for an autoregressive model. The methodology is illustrated using both simulated and real data.

Suggested Citation

  • Richard Gerlach & Chris Carter & Robert Kohn, 1999. "Diagnostics for Time Series Analysis," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(3), pages 309-330, May.
    • Handle: RePEc:bla:jtsera:v:20:y:1999:i:3:p:309-330
    DOI: 10.1111/1467-9892.00139
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    Citations

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    Cited by:

    1. Carlos A. Abanto‐Valle & Roland Langrock & Ming‐Hui Chen & Michel V. Cardoso, 2017. "Maximum likelihood estimation for stochastic volatility in mean models with heavy‐tailed distributions," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 33(4), pages 394-408, August.
    2. Sylvia Kaufmann & Sylvia Frühwirth‐Schnatter, 2002. "Bayesian analysis of switching ARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(4), pages 425-458, July.
    3. Chen, Cathy W.S. & Gerlach, Richard & So, Mike K.P., 2006. "Comparison of nonnested asymmetric heteroskedastic models," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2164-2178, December.
    4. Neil Shephard & Michael K. Pitt, 1999. "Auxiliary variable based particle filters," Economics Series Working Papers 1999-W13, University of Oxford, Department of Economics.
    5. Pitt, Michael K., 2002. "Smooth particle filters for likelihood evaluation and maximisation," Economic Research Papers 269464, University of Warwick - Department of Economics.
    6. Chen, Cathy W.S. & So, Mike K.P., 2006. "On a threshold heteroscedastic model," International Journal of Forecasting, Elsevier, vol. 22(1), pages 73-89.
    7. Gerlach, Richard & Chen, Cathy W.S. & Lin, Doris S.Y. & Huang, Ming-Hsiang, 2006. "Asymmetric responses of international stock markets to trading volume," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(2), pages 422-444.
    8. Cathy Chen & Feng Liu & Richard Gerlach, 2011. "Bayesian subset selection for threshold autoregressive moving-average models," Computational Statistics, Springer, vol. 26(1), pages 1-30, March.
    9. Cathy W. S. Chen & Richard H. Gerlach & Ann M. H. Lin, 2010. "Falling and explosive, dormant, and rising markets via multiple‐regime financial time series models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(1), pages 28-49, January.
    10. Victor Guerrero, 2005. "Restricted estimation of an adjusted time series: application to Mexico's industrial production index," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(2), pages 157-177.
    11. Gerlach, Richard & Tuyl, Frank, 2006. "MCMC methods for comparing stochastic volatility and GARCH models," International Journal of Forecasting, Elsevier, vol. 22(1), pages 91-107.
    12. David Ardia, 2009. "Bayesian estimation of a Markov-switching threshold asymmetric GARCH model with Student-t innovations," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 105-126, March.
    13. Pitt, Michael K, 2002. "Smooth Particle Filters for Likelihood Evaluation and Maximisation," The Warwick Economics Research Paper Series (TWERPS) 651, University of Warwick, Department of Economics.
    14. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
    15. Mr. Noureddine Krichene, 2003. "Modeling Stochastic Volatility with Application to Stock Returns," IMF Working Papers 2003/125, International Monetary Fund.
    16. Hella, Heikki, 2003. "On robust ESACF identification of mixed ARIMA models," Bank of Finland Scientific Monographs, Bank of Finland, volume 0, number sm2003_027, July.

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