Approximation to the finite sample distribution of a sufficient estimator of the coefficient in a non-stationary AR(1) model

ABRIL, JUAN CARLOS

Pakistan Journal of Statistics

Pakistan Journal of Statistics

Lugar: Lahore, Pakistan; Año: 2007 vol. 23 p. 231 - 240

1012-9367

          The problem of unit roots in time series has become the centre of many papers in theoretical and applied econometric. It has its own interest for theoretical researchers due to the asymptotic effects over the properties of estimators and tests statistics. For the applied work, establishing the presence of unit roots is still the cornerstone of the analysis of possible cointegrated systems: firstly as a preliminary tool for testing the integration of the variables of interest, and secondly as a cointegration tests for itself. In this work we consider the model                                    yt = ryt-1 + et ,      t = 1, 2, …,n, where y0 = 0, the et’s are independent and identically distributed (iid) N(0, s2), çrç£1 and we study approximations of second and third order to the distribution of the estimator of the coefficient r. Firstly we develop the general case for all r, such that çrç£1 and then we particularize for the non-stationary case when there is a unit root, that is when r = 1. The approximations are obtained using using Durbin’s (1980a) method for approximating densities of sufficient estimators. A comparison between our approximations and Monte Carlo simulations is made in order to evaluate the performance of the formers.