Asymptotics For Estimation Of Truncated Infinite-Dimensional Quantile Regressions
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.
|Date of creation:||Aug 2006|
|Contact details of provider:|| Postal: 855 Sherbrooke St. W., Montréal, Québec, H3A 2T7|
Phone: (514) 398-3030
Fax: (514) 398-4938
Web page: http://www.repec.mcgill.ca
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- repec:cup:etheor:v:12:y:1996:i:1:p:61-87 is not listed on IDEAS
- 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.
- Sílvia Gonçalves & Lutz Kilian, 2003. "Asymptotic and Bootstrap Inference for AR( Infinite ) Processes with Conditional Heteroskedasticity," CIRANO Working Papers 2003s-28, CIRANO.
- 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.
- repec:cup:etheor:v:7:y:1991:i:4:p:450-63 is not listed on IDEAS
- 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.
- repec:cup:etheor:v:7:y:1991:i:2:p:186-99 is not listed on IDEAS
- 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.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Saikkonen, Pentti & Lütkepohl, HELMUT, 1996. "Infinite-Order Cointegrated Vector Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 12(05), pages 814-844, December.
- repec:cup:etheor:v:11:y:1995:i:5:p:912-51 is not listed on IDEAS
- 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.
When requesting a correction, please mention this item's handle: RePEc:mcl:mclwop:2006-16. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shama Rangwala)
If references are entirely missing, you can add them using this form.