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.

Least absolute deviation estimates in autoregression with infinite variance

1979 ◽  
Vol 16 (01) ◽  
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 L 1 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 Indirect Inference Estimation of Spatial Autoregressions

Econometrics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 34
Author(s):  
Yong Bao ◽  
Xiaotian Liu ◽  
Lihong Yang
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Asymptotic Distribution ◽  
Monte Carlo Study ◽  
Ordinary Least Squares ◽  
Indirect Inference ◽  
Finite Sample ◽  
Spatial Unit ◽  
Asymptotically Normal ◽  
Distribution Result

The ordinary least squares (OLS) estimator for spatial autoregressions may be consistent as pointed out by Lee (2002), provided that each spatial unit is influenced aggregately by a significant portion of the total units. This paper presents a unified asymptotic distribution result of the properly recentered OLS estimator and proposes a new estimator that is based on the indirect inference (II) procedure. The resulting estimator can always be used regardless of the degree of aggregate influence on each spatial unit from other units and is consistent and asymptotically normal. The new estimator does not rely on distributional assumptions and is robust to unknown heteroscedasticity. Its good finite-sample performance, in comparison with existing estimators that are also robust to heteroscedasticity, is demonstrated by a Monte Carlo study.

LM TESTS IN THE PRESENCE OF NON-NORMAL ERROR DISTRIBUTIONS

2000 ◽  
Vol 16 (2) ◽  
pp. 249-261 ◽  
Author(s):  
Marilena Furno
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Study ◽  
Ordinary Least Squares ◽  
Conditional Heteroskedasticity ◽  
Absolute Deviation ◽  
Absolute Value ◽  
Lm Tests ◽  
Normal Error ◽  
Error Distributions ◽  
Squared Residuals

The paper considers different versions of the Lagrange multiplier (LM) tests for autocorrelation and/or for conditional heteroskedasticity. These versions differ in terms of the residuals, and of the functions of the residuals, used to build the tests. In particular, we compare ordinary least squares versus least absolute deviation (LAD) residuals, and we compare squared residuals versus their absolute value. We show that the LM tests based on LAD residuals are asymptotically distributed as a χ2 and that these tests are robust to nonnormality. The Monte Carlo study provides evidence in favor of the LAD residuals, and of the absolute value of the LAD residuals, to build the LM tests here discussed.

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