EDGEWORTH APPROXIMATION IN THE AR(1) PROCESS WITH SOME POSSIBLY NONZERO INITIAL VALUE

Abstract

This paper shows the validity of the (arbitrary) higher order Edgeworth expansion for the distribution of estimators of the coefficient parameter θ∈(−1, 1) in the AR(1) process {X_t} with a possibly nonzero initial value X₀=x. The stationary case of X₀∼N(0, 1/(1−θ²)) is also treated.