Least Absolute Deviation Estimation of Multi-Equation Linear Econometric Models: A Study Based on Monte Carlo Experiments

2003 ◽  
Author(s):  
S. K. Mishra ◽  
Madhuchhanda Dasgupta
Keyword(s):  
Monte Carlo ◽  
Econometric Models ◽  
Least Absolute Deviation ◽  
Absolute Deviation ◽  
Least Absolute Deviation Estimation ◽  
Monte Carlo Experiments

Least absolute deviation estimates in autoregression with infinite variance

1979 ◽  
Vol 16 (1) ◽  
pp. 104-116 ◽  
Author(s):  
S. Gross ◽  
W. L. Steiger
Keyword(s):  
Monte Carlo ◽  
Convergence Rate ◽  
Least Squares ◽  
Finite Order ◽  
Monte Carlo Study ◽  
Least Squares Estimator ◽  
Infinite Variance ◽  
Least Absolute Deviation ◽  
Absolute Deviation ◽  
Strongly Consistent

We consider an L1 analogue of the least squares estimator for the parameters of stationary, finite-order autoregressions. This estimator, the least absolute deviation (LAD), is shown to be strongly consistent via a result that may have independent interest. The striking feature is that the conditions are so mild as to include processes with infinite variance, notably the stationary, finite autoregressions driven by stable increments in Lα, α > 1. Finally, sampling properties of LAD are compared to those of least squares. Together with a known convergence rate result for least squares, the Monte Carlo study provides evidence for a conjecture on the convergence rate of LAD.

scholarly journals LEAST ABSOLUTE DEVIATION ESTIMATION FOR UNIT ROOT PROCESSES WITH GARCH ERRORS

2009 ◽  
Vol 25 (5) ◽  
pp. 1208-1227 ◽  
Author(s):  
Guodong Li ◽  
Wai Keung Li
Keyword(s):  
Unit Root ◽  
Asymptotic Properties ◽  
Maximum Likelihood Estimators ◽  
Unit Root Tests ◽  
Order Moment ◽  
Least Absolute Deviation ◽  
Absolute Deviation ◽  
Least Absolute Deviation Estimation ◽  
Heavy Tailed ◽  
Quasi Maximum Likelihood

This paper considers a local least absolute deviation estimation for unit root processes with generalized autoregressive conditional heteroskedastic (GARCH) errors and derives its asymptotic properties under only finite second-order moment for both errors and innovations. When the innovations are symmetrically distributed, the asymptotic distribution of the estimated unit root is shown to be a functional of a bivariate Brownian motion, and then two unit root tests are derived. The simulation results demonstrate that the tests outperform those based on the Gaussian quasi maximum likelihood estimators with heavy-tailed innovations and those based on the simple least absolute deviation estimators.

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