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Asymptotics For Estimation Of Truncated Infinite-Dimensional Quantile Regressions

  • Serguei Zernov

    ()

  • Victoria Zindle-Walsh

    ()

  • John Galbraith

    ()

Many processes can be represented in a simple form as infinite-order linear series. In such cases, an approximate model is often derived as a truncation of the infinite-order process, for estimation on the finite sample. The literature contains a number of asymptotic distributional results for least squares estimation of such finite truncations, but for quantile estimation, only results for finite-order processes are available at a level of generality that accommodates time series processes. Here we establish consistency and asymptotic normality for conditional quantile estimation of truncations of such infinite-order linear models, with the truncation order increasing in sample size. The proofs use the generalized functions approach and allow for a wide range of time series models as well as other forms of regression model. As an example, many time series processes may be represented as an AR(?) or an MA(?); here we use a simulation to illustrate the degree of conformity of finite sample results with the asymptotics, in case of a truncated AR representation of a moving average.

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File URL: http://www.mcgill.ca/files/economics/asymptoticsforestimation.pdf
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Paper provided by McGill University, Department of Economics in its series Departmental Working Papers with number 2006-16.

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Length: 13 pages
Date of creation: Aug 2006
Date of revision:
Handle: RePEc:mcl:mclwop:2006-16
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  1. Braun, Phillip A. & Mittnik, Stefan, 1993. "Misspecifications in vector autoregressions and their effects on impulse responses and variance decompositions," Journal of Econometrics, Elsevier, vol. 59(3), pages 319-341, October.
  2. Roger Koenker & Zhijie Xiao, 2004. "Unit Root Quantile Autoregression Inference," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 775-787, January.
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  8. Saikkonen, Pentti & Lütkepohl, HELMUT, 1996. "Infinite-Order Cointegrated Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(05), pages 814-844, December.
  9. Lutkepohl, Helmut & Saikkonen, Pentti, 1997. "Impulse response analysis in infinite order cointegrated vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 127-157, November.
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  11. Sílvia Gonçalves & Lutz Kilian, 2003. "Asymptotic and Bootstrap Inference for AR( Infinite ) Processes with Conditional Heteroskedasticity," CIRANO Working Papers 2003s-28, CIRANO.
  12. Phillips, Peter C.B., 1995. "Robust Nonstationary Regression," Econometric Theory, Cambridge University Press, vol. 11(05), pages 912-951, October.
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  14. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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