A sharp analysis on the asymptotic behavior of the Durbin-Watson statistic for the first-order autoregressive process
BERCU, Bernard
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
PROIA, Frédéric
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
BERCU, Bernard
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
PROIA, Frédéric
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
< Leer menos
Institut de Mathématiques de Bordeaux [IMB]
Advanced Learning Evolutionary Algorithms [ALEA]
Idioma
en
Article de revue
Este ítem está publicado en
ESAIM: Probability and Statistics. 2013, vol. 17, p. 500-530
EDP Sciences
Resumen en inglés
The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin-Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by ...Leer más >
The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin-Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We establish the almost sure convergence and the asymptotic normality for both the least squares estimator of the unknown parameter of the autoregressive process as well as for the serial correlation estimator associated to the driven noise. In addition, the almost sure rates of convergence of our estimates are also provided. It allows us to establish the almost sure convergence and the asymptotic normality for the Durbin-Watson statistic. Finally, we propose a new bilateral statistical test for residual autocorrelation.< Leer menos
Palabras clave en inglés
Durbin-Watson statistic
Autoregressive process
Residual autocorrelation
Statistical test for serial correlation
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