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Asymptotics of an Explosive Autoregression under Dependence

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  • Kasper Sunn Blumensaat

Abstract

We generalize the convergence results of an explosive autoregression, pioneered in Anderson (1959), in three ways: First, we demonstrate that the centered least-squares estimator converges geometrically to a ratio of limits, even in settings where the innovations are correlated and not centered around zero. Secondly, we demonstrate that the requirement of independent innovations in Anderson (1959), Theorem 2.3, can be relaxed to $\alpha$-mixing. Third, we provide an autocorrelation-robust feasible test statistic for the explosive parameter under Gaussian ARMA innovations.

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  • Kasper Sunn Blumensaat, 2026. "Asymptotics of an Explosive Autoregression under Dependence," Papers 2606.09531, arXiv.org.
    • Handle: RePEc:arx:papers:2606.09531
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    References listed on IDEAS

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    1. Nielsen, Bent, 2010. "Analysis Of Coexplosive Processes," Econometric Theory, Cambridge University Press, vol. 26(3), pages 882-915, June.
    2. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
    3. 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.
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