Regression quantiles for unstable autoregressive models
AbstractThis 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. It involves stochastic integrals in terms of a sequence 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 89 (2004)
Issue (Month): 2 (May)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
Other versions of this item:
- Shiqing Ling & Michael McAleer, 2003. "Regression Quantiles for Unstable Autoregressive Models," CIRJE F-Series CIRJE-F-205, CIRJE, Faculty of Economics, University of Tokyo.
- Ling, S. & McAleer, M., 2001. "Regression Quantiles for Unstable Autoregressive Models," ISER Discussion Paper 0526, Institute of Social and Economic Research, Osaka University.
- C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
- C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
- C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
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