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LAD Asymptotics under Conditional Heteroskedasticity with Possibly Infinite Error Densities

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Abstract

Least absolute deviations (LAD) estimation of linear time-series models is considered under conditional heteroskedasticity and serial correlation. The limit theory of the LAD estimator is obtained without assuming the finite density condition for the errors that is required in standard LAD asymptotics. The results are particularly useful in application of LAD estimation to financial time series data.

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File URL: http://cowles.econ.yale.edu/P/cd/d17a/d1703.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1703.

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Length: 10 pages
Date of creation: Jun 2009
Date of revision:
Publication status: Published in Econometric Theory (2010), 26(3): 953-962
Handle: RePEc:cwl:cwldpp:1703

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Asymptotic leptokurtosis; Convex function; Infinite density; Least absolute deviations; Median; Weak convergence;

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  1. Phillips, P.C.B., 1991. "A Shortcut to LAD Estimator Asymptotics," Econometric Theory, Cambridge University Press, vol. 7(04), pages 450-463, December.
  2. Chirok Han & Jin Seo Cho & Peter C.B. Phillips, 2009. "Infinite Density at the Median and the Typical Shape of Stock Return Distributions," Cowles Foundation Discussion Papers 1701, Cowles Foundation for Research in Economics, Yale University.
  3. Rogers, Alan J., 2001. "Least Absolute Deviations Regression Under Nonstandard Conditions," Econometric Theory, Cambridge University Press, vol. 17(04), pages 820-852, August.
  4. 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.
  5. Bose, Arup & Chatterjee, Snigdhansu, 2001. "Generalised bootstrap in non-regular M-estimation problems," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 319-328, December.
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