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Asymptotic Theory for Unit Root Moderate Deviations in Quantile Autoregressions and Predictive Regressions

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  • Christis Katsouris

Abstract

We establish the asymptotic theory in quantile autoregression when the model parameter is specified with respect to moderate deviations from the unit boundary of the form (1 + c / k) with a convergence sequence that diverges at a rate slower than the sample size n. Then, extending the framework proposed by Phillips and Magdalinos (2007), we consider the limit theory for the near-stationary and the near-explosive cases when the model is estimated with a conditional quantile specification function and model parameters are quantile-dependent. Additionally, a Bahadur-type representation and limiting distributions based on the M-estimators of the model parameters are derived. Specifically, we show that the serial correlation coefficient converges in distribution to a ratio of two independent random variables. Monte Carlo simulations illustrate the finite-sample performance of the estimation procedure under investigation.

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  • Christis Katsouris, 2022. "Asymptotic Theory for Unit Root Moderate Deviations in Quantile Autoregressions and Predictive Regressions," Papers 2204.02073, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:2204.02073
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