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On limiting distributions in explosive autoregressive processes

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  • Monsour, Michael J.
  • Mikulski, Piotr W.

Abstract

The limiting distribution is obtained for the maximum likelihood estimator in the AR(p) process with a random and nonrandom normalization and all characteristic roots outside the unit circle, purely explosive process. Though these results have been in the literature, proofs have been omitted. A detailed proof of these results will be presented. With a random normalization the limiting distribution is multivariate standard normal.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:37:y:1998:i:2:p:141-147
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    References listed on IDEAS

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    1. Lai, T. L. & Wei, C. Z., 1983. "Asymptotic properties of general autoregressive models and strong consistency of least-squares estimates of their parameters," Journal of Multivariate Analysis, Elsevier, vol. 13(1), pages 1-23, March.
    2. Stigum, Bernt P., 1974. "Asymptotic properties of dynamic stochastic parameter estimates (III)," Journal of Multivariate Analysis, Elsevier, vol. 4(4), pages 351-381, December.
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    Cited by:

    1. 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.
    2. Victor Konev & Bogdan Nazarenko, 2020. "Sequential fixed accuracy estimation for nonstationary autoregressive processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 235-264, February.
    3. Maller, R. A., 2003. "Asymptotics of regressions with stationary and nonstationary residuals," Stochastic Processes and their Applications, Elsevier, vol. 105(1), pages 33-67, May.
    4. Monsour, Michael J., 2016. "Decomposition of an autoregressive process into first order processes," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 295-314.

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