Regression Quantiles for Unstable Autoregressive Models

Shiqing Ling (maling@ust.hk) and Michael McAleer

No CIRJE-F-205, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: This paper investigates regression quantiles(RQ) for unstable autoregressive models. This uniform Bahadur representation of the RQ process is obtained. The joint asymptotic distribution of the RQ process is derived in a unified manner for all types of characteristic roots on or outside the unit circle. It involves stochastic integrals in terms of a wequence of independent and identically distributed multivariate Brownian motions with correlated components. The related L -estimator is also discussed. The asymptotic distributions of the RQ and the L -estimator corresponding to the nonstationary componentwise arguments can be transformed into a function of a normal random variable and a sequence of i.i.d. univariate Brownian motions. This is different from the analysis based on the lSE in the literature. As an auxiliary theorem, a weak convergence of a randomly weighted residual empirical process to the stochastic integral of a Kiefer process is established. The results obtained in this paper provide an asymptotic theory for nonstationary time series processes, which can be used to construct robust unit root tests.

Pages: 28 pages
Date: 2003-03
New Economics Papers: this item is included in nep-ecm and nep-ets
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Related works:
Journal Article: Regression quantiles for unstable autoregressive models (2004)
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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2003cf205

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