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Hierarchical equilibria of branching populations

Author

Listed:
  • Hao Yu

    (Department of Statistical and Actuarial Sciences, University of Western Ontario)

Abstract

In this paper we study high moment partial sum processes based on residuals of a stationary ARMA model with or without a unknown mean parameter. We show that they can be approximated in probability by the analogous processes which are obtained from the independent and identically distributed (iid) errors of the ARMA model. However, if a unknown mean parameter is used, there will be an additional term that depends on model parameters and a mean estimator. But, when properly normalized, this additional term will be cancelled out. Thus they converge weakly to the same Gaussian processes as if the residuals were iid. Applications to changepoint problems and goodness-of-fit are considered, in particular CUSUM statistics for testing ARMA model structure changes and the Jarque-Bera omnibus statistic for testing normality of the unobservable error distribution of an ARMA model.

Suggested Citation

  • Hao Yu, 2003. "Hierarchical equilibria of branching populations," RePAd Working Paper Series lrsp-TRS391, Département des sciences administratives, UQO.
    • Handle: RePEc:pqs:wpaper:0182005
    as

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    File URL: http://www.repad.org/ca/on/lrsp/TRS391.pdf
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    References listed on IDEAS

    as
    1. Jushan Bai, 1993. "On The Partial Sums Of Residuals In Autoregressive And Moving Average Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(3), pages 247-260, May.
    2. Kulperger, R. J., 1985. "On the residuals of autoregressive processes and polynomial regression," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 107-118, December.
    3. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    4. J. Kreiss, 1991. "Estimation of the distribution function of noise in stationary processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 38(1), pages 285-297, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    ARMA; residuals; high moment partial sum process; weak convergence; CUSUM; omnibus; skewness; kurtosis; (sqare root)n consistency.;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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