Aproximación de segundo orden a la distribución de un estimador general del coeficiente de un modelo AR(1)

ABRIL, JUAN CARLOS

Villa Giardino

Congreso; XXIII Coloquio Argentino de Estadística; 1995

We define as a general estimator of the coefficient of a non-circular first order stochastic difference equation, where . When a = 1 and b = 0 we have the least squares estimator which is exactly equal to the conditional maximum likelihood estimator, when a = 1 and b = 1 we have the estimator obtained by solving the sample Yule-Walker equations, and when a = b = 0 we have the approximate maximum likelihood estimator. Our conjecture is that the exact maximum likelihood estimator is contemplated in this general estimator. In this work we investigate the third order approximation to the distribution of the above given estimator using Edgeworth series expansions. The results so obtained cover the different cases of estimators usually used for practical purposes.