Asymptotics for estimation of quantile regressions with truncated infinite-dimensional processes
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, results are not available at a level of generality that accommodates time series models used as finite approximations to processes of potentially unbounded order. 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. We focus on estimation of the model at a given quantile. 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. The results are illustrated with both analytical and simulation examples.
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Volume (Year): 100 (2009)
Issue (Month): 3 (March)
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- Herce, Miguel A., 1996. "Asymptotic Theory of LAD Estimation in a Unit Root Process with Finite Variance Errors," Econometric Theory, Cambridge University Press, vol. 12(01), pages 129-153, March.
- Knight, Keith, 1991. "Limit Theory for M-Estimates in an Integrated Infinite Variance," Econometric Theory, Cambridge University Press, vol. 7(02), pages 200-212, June.
- Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(05), pages 793-813, December.
- Koenker,Roger, 2005.
Cambridge University Press, number 9780521608275, December.
- 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.
- Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
- 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.
- H. Lütkepohl & P. Saikkonen, 1995. "Impulse Response Analysis in Infinite Order Cointegrated Vector Autoregressive Processes," SFB 373 Discussion Papers 1995,11, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- 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.
- Lütkepohl, Helmut & POSKITT, D.S., 1996. "Testing for Causation Using Infinite Order Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(01), pages 61-87, March.
- Portnoy, Stephen, 1991. "Asymptotic behavior of regression quantiles in non-stationary, dependent cases," Journal of Multivariate Analysis, Elsevier, vol. 38(1), pages 100-113, July.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Davis, Richard A. & Knight, Keith & Liu, Jian, 1992. "M-estimation for autoregressions with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 145-180, February.
- Saikkonen, Pentti & Lütkepohl, HELMUT, 1996. "Infinite-Order Cointegrated Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(05), pages 814-844, December.
- Peter C.B. Phillips, 1993.
"Robust Nonstationary Regression,"
Cowles Foundation Discussion Papers
1064, Cowles Foundation for Research in Economics, Yale University.
- Phillips, P.C.B., 1991.
"A Shortcut to LAD Estimator Asymptotics,"
Cambridge University Press, vol. 7(04), pages 450-463, December.
- Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
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