CIRJE-F-205 | "Regression Quantiles for Unstable Autoregressive Models" |
Author Name | Ling, Shiqing and Michael McAleer |
Date | March 2003 |
Full Paper | PDF file@ |
Remarks | Subsequently published in Journal of Multivariate Analysis. |
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. |