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Publisher: Elsevier.

Issued date: 2000-02-01

Citation: Journal of Statistical Planning and Inference, 1 Feb. 2000 , 83 2, 347–367.

ISSN: 0378-3758

DOI: 10.1016-S0378-37589900101-9

Publisher version: http:-dx.doi.org-10.1016-S0378-37589900101-9

Keywords: Autoregressive process , Bootstrap , Least absolute deviation , Unit root

Abstract:In this paper we propose a new bootstrap test for unit roots in first-order autoregressive models based on least absolute deviation LAD estimators. It is well known that the behaviour of this estimator when the distribution is heavy tailed is very good compaIn this paper we propose a new bootstrap test for unit roots in first-order autoregressive models based on least absolute deviation LAD estimators. It is well known that the behaviour of this estimator when the distribution is heavy tailed is very good compared with least-squares estimation. The innovations distribution dependence of the LAD asymptotic law is overcome using bootstrap, which automatically approaches the target distribution. Our strategy avoids the usual problem of estimating the variance matrix and the density at zero, and makes also unnecessary the construction of distribution free statistics through linear combinations with the least-squares estimator. We provide the bootstrap functional limit theory necessary to prove the asymptotic validity of the procedure. Moreover, a large simulation study shows that our test has very good power behaviour compared with others proposed in the literature.+-





Author: Moreno, Marta; Romo Urroz, Juan

Source: http://e-archivo.uc3m.es


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Universidad Carlos III de Madrid Repositorio institucional e-Archivo http:--e-archivo.uc3m.es Departamento de Estadística DES - Artículos de Revistas 2000-02-01 Bootstrap tests for unit roots based on LAD estimation. Moreno, Marta Elsevier. þÿJournal of Statistical Planning and Inference, (1 Feb.
2000) , 83 (2), 347 367. http:--hdl.handle.net-10016-14849 Descargado de e-Archivo, repositorio institucional de la Universidad Carlos III de Madrid Bootstrap tests for unit roots based on LAD estimation Marta Moreno 1 , Juan Romo ∗; 2 Departamento de Estadstica, Universidad Carlos III de Madrid, c=Madrid 26, 28903 Getafe, Madrid, Spain Received 11 May 1998; accepted 2 April 1999 Abstract In this paper we propose a new bootstrap test for unit roots in rst-order autoregressive models based on least absolute deviation (LAD) estimators.
It is well known that the behaviour of this estimator when the distribution is heavy tailed is very good compared with least-squares estimation.
The innovations distribution dependence of the LAD asymptotic law is overcome using bootstrap, which automatically approaches the target distribution.
Our strategy avoids the usual problem of estimating the variance matrix and the density at zero, and makes also unnecessary the construction of distribution free statistics through linear combinations with the least-squares estimator.
We provide the bootstrap functional limit theory necessary to prove the asymptotic validity of the procedure.
Moreover, a large simulation study shows that our test has very good power behaviour compared with others proposed in the literature. MSC: 62E20; 62E25; 62M10 Keywords: Autoregressive process; Bootstrap; Least absolute deviation; Unit root 1.
Introduction Let {Xt }; t = 1; 2; : : : be a rst-order autoregressive process de ned by Xt = Xt−1 ut ; X0 = 0; where {ut } is a sequence of independent and identically distributed random variables with E(ut ) = 0 and Var(ut ) = 12 ¡ ∞.
We are inter...





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