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Cowles Foundation Discussion Papers

2009

Least absolute deviations

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Full-Text Articles in Economics

Infinite Density At The Median And The Typical Shape Of Stock Return Distributions, Chirok Han, Jin Seo Cho, Peter C.B. Phillips Jun 2009

Infinite Density At The Median And The Typical Shape Of Stock Return Distributions, Chirok Han, Jin Seo Cho, Peter C.B. Phillips

Cowles Foundation Discussion Papers

Statistics are developed to test for the presence of an asymptotic discontinuity (or infinite density or peakedness) in a probability density at the median. The approach makes use of work by Knight (1998) on L 1 estimation asymptotics in conjunction with non-parametric kernel density estimation methods. The size and power of the tests are assessed, and conditions under which the tests have good performance are explored in simulations. The new methods are applied to stock returns of leading companies across major U.S. industry groups. The results confirm the presence of infinite density at the median as a new significant empirical …


Lad Asymptotics Under Conditional Heteroskedasticity With Possibly Infinite Error Densities, Jin Seo Cho, Chirok Han, Peter C.B. Phillips Jun 2009

Lad Asymptotics Under Conditional Heteroskedasticity With Possibly Infinite Error Densities, Jin Seo Cho, Chirok Han, Peter C.B. Phillips

Cowles Foundation Discussion Papers

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.