Econometrica: Sep, 1984, Volume 52, Issue 5

Approximation to the Finite Sample Distribution for Nonstable First Order Stochastic Difference Equations

https://doi.org/0012-9682(198409)52:5<1271:ATTFSD>2.0.CO;2-B
p. 1271-1290

S. E. Satchell

This paper considers approximations to the distribution of the least squares estimator of @a in the model @y"t = @a@y"t"-"1 + @u"t where the @u"t are independently distributed N(0, @s^2) and @y"0 is fixed. An Edgeworth approximation for this case is calculated, and compared with results for the stationary case. For |@a| > 1 and fixed @y"0, the asymptotic distribution is found in closed form; when |@a| > 1 and @y"0 = 0, an Edgeworth-type approximation is again calculated; this is compared with exact results.