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A note on limit theory for mildly stationary autoregression with a heavy-tailed GARCH error process

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  • Hwang, Eunju

Abstract

A first-order mildly stationary autoregression with a heavy-tailed GARCH error process is considered to study the limit theory for the least squared estimator of the autoregression coefficient ρ=ρn∈[0,1). A Gaussian limit theory is established as ρn converges to the unity as n→∞, with rate condition (1−ρn)n→∞, as in Giraitis and Philips (2006), who have discussed the limit theory in case that errors are martingale difference sequences. This work addresses asymptotic results in a case of heavy-tailed GARCH errors, and extends the existing one by allowing errors to follow heavy-tailed process as well as conditional heteroscedasticity.

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  • Hwang, Eunju, 2019. "A note on limit theory for mildly stationary autoregression with a heavy-tailed GARCH error process," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 59-68.
    • Handle: RePEc:eee:stapro:v:152:y:2019:i:c:p:59-68
    DOI: 10.1016/j.spl.2019.04.009
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    1. Liudas Giraitis & Peter C. B. Phillips, 2006. "Uniform Limit Theory for Stationary Autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 51-60, January.
    2. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
    3. Fei, Yijie, 2018. "Limit theory for mildly integrated process with intercept," Economics Letters, Elsevier, vol. 163(C), pages 98-101.
    4. Zhang, Rongmao & Ling, Shiqing, 2015. "Asymptotic Inference For Ar Models With Heavy-Tailed G-Garch Noises," Econometric Theory, Cambridge University Press, vol. 31(4), pages 880-890, August.
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    Cited by:

    1. Eunju Hwang, 2021. "Limit Theory for Stationary Autoregression with Heavy-Tailed Augmented GARCH Innovations," Mathematics, MDPI, vol. 9(8), pages 1-10, April.

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