J. Japan Statist. Soc., Vol. 32 (No. 2), pp. 209-237, 2002

Edgeworth Approximation in The AR(1) Process with Some Possibly Nonzero Initial Value

Yoshihide Kakizawa

Abstract. This paper shows the validity of the (arbitrary) higher order Edgeworth expansion for the distribution of estimators of the coefficient parameter q (-1,1) in the AR(1) process {Xt} with a possibly nonzero initial value X0 = x. The stationary case of X0 ~ N(0,1/(1 - q2)) is also treated.

Key words and phrases: Edgeworth expansion, Berry-Esseen bound, moderate deviation, AR(1) process.

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