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Arbitrary initial values and random norm for explosive AR(1) processes generated by stationary errors


  • Hwang, S.Y.


This article is concerned with a broad class of explosive AR(1) models. Allowing stationary dependence on the error process, we do not restrict ourselves to independent and identically distributed errors. The model accommodates, as special cases, GARCH errors, AR(1) errors and Gaussian ARMA errors. The error distribution is permitted to be non-normal. To circumvent the effect of initial values, the limit distribution of the least squares estimate using a random norm (rather than a constant norm) is derived. It is shown that the limit distribution using a random norm is free from the initial value provided the error is symmetrically distributed about zero.

Suggested Citation

  • Hwang, S.Y., 2013. "Arbitrary initial values and random norm for explosive AR(1) processes generated by stationary errors," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 127-134.
  • Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:127-134
    DOI: 10.1016/j.spl.2012.08.022

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    References listed on IDEAS

    1. Hwang, S.Y. & Basawa, I.V., 2011. "Asymptotic optimal inference for multivariate branching-Markov processes via martingale estimating functions and mixed normality," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1018-1031, July.
    2. Hwang, S.Y. & Kim, S. & Lee, S.D. & Basawa, I.V., 2007. "Generalized least squares estimation for explosive AR(1) processes with conditionally heteroscedastic errors," Statistics & Probability Letters, Elsevier, vol. 77(13), pages 1439-1448, July.
    3. S. Y. Hwang & I. V. Basawa, 2005. "Explosive Random-Coefficient AR(1) Processes and Related Asymptotics for Least-Squares Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 807-824, November.
    4. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(05), pages 818-887, October.
    5. Monsour, Michael J. & Mikulski, Piotr W., 1998. "On limiting distributions in explosive autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 37(2), pages 141-147, February.
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    Cited by:

    1. Christoph P. Kustosz & Anne Leucht & Christine H. M√úller, 2016. "Tests Based on Simplicial Depth for AR(1) Models With Explosion," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(6), pages 763-784, November.


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