M-estimation for Moderate Deviations From a Unit Root

2014 ◽  
Vol 44 (3) ◽  
pp. 476-485 ◽  
Author(s):  
Xin-Bing Kong
Keyword(s):  
Unit Root ◽  
Moderate Deviations ◽  
M Estimation

scholarly journals Limit theory for moderate deviations from a unit root

2007 ◽  
Vol 136 (1) ◽  
pp. 115-130 ◽  
Author(s):  
Peter C.B. Phillips ◽  
Tassos Magdalinos
Keyword(s):  
Unit Root ◽  
Moderate Deviations ◽  
Limit Theory

scholarly journals ASYMPTOTIC THEORY FOR KERNEL ESTIMATORS UNDER MODERATE DEVIATIONS FROM A UNIT ROOT, WITH AN APPLICATION TO THE ASYMPTOTIC SIZE OF NONPARAMETRIC TESTS

2019 ◽  
Vol 36 (4) ◽  
pp. 559-582
Author(s):  
James A. Duffy
Keyword(s):  
Unit Root ◽  
Regression Models ◽  
Asymptotic Theory ◽  
Kernel Density ◽  
Nonparametric Tests ◽  
Moderate Deviations ◽  
Autoregressive Processes ◽  
Predictive Regression ◽  
Asymptotic Size ◽  
Rejection Probability

We provide new asymptotic theory for kernel density estimators, when these are applied to autoregressive processes exhibiting moderate deviations from a unit root. This fills a gap in the existing literature, which has to date considered only nearly integrated and stationary autoregressive processes. These results have applications to nonparametric predictive regression models. In particular, we show that the null rejection probability of a nonparametric t test is controlled uniformly in the degree of persistence of the regressor. This provides a rigorous justification for the validity of the usual nonparametric inferential procedures, even in cases where regressors may be highly persistent.

M-ESTIMATION FOR A SPATIAL UNILATERAL AUTOREGRESSIVE MODEL WITH INFINITE VARIANCE INNOVATIONS

2010 ◽  
Vol 26 (6) ◽  
pp. 1663-1682 ◽  
Author(s):  
S.M. Roknossadati ◽  
M. Zarepour
Keyword(s):  
Simulation Study ◽  
Unit Root ◽  
Autoregressive Model ◽  
Domain Of Attraction ◽  
Infinite Variance ◽  
Stable Law ◽  
Limiting Behavior ◽  
Asymptotically Normal ◽  
M Estimation ◽  
Unit Root Models

We study the limiting behavior of the M-estimators of parameters for a spatial unilateral autoregressive model with independent and identically distributed innovations in the domain of attraction of a stable law with index α ∈ (0, 2]. Both stationary and unit root models and some extensions are considered. It is also shown that self-normalized M-estimators are asymptotically normal. A numerical example and a simulation study are also given.

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