Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/92718 
Year of Publication: 
2001
Series/Report no.: 
ISER Discussion Paper No. 526
Publisher: 
Osaka University, Institute of Social and Economic Research (ISER), Osaka
Abstract: 
This paper investigates regression quantiles (RQ) for unstable autoregressive models. The 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. Unlike the results already available for the regression and stationary autoregression quantiles, the joint asymptotic distribution involves stochastic integrals in terms of a series of independent and identically distributed multivariate Brownian motions with correlated components. The related L-estimator is also discussed. 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.
Document Type: 
Working Paper

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