Critical values for testing a unit root in finite samples from the MA(1)

Abstract

This study, using a certain simulation strategy, for the exact maximum likelihood estimator of θ from the MA(1), estimates appropriate percentiles, together with their standard errors, offering a new set of critical values for testing in finite samples H₀: θ = −1, against H₁: θ>−1. In this way, appropriate regions for rejecting the null or being in uncertainty are defined, regardless of the values of MA(1) parameters. The new set of critical values produce both actual level of significance close to the nominal one and, when θ is not very close to −1, comparable power with the up to now suggested asymptotic values. These asymptotic values, unfortunately, lead to actual level of significance considerably greater than the nominal one, especially in large samples.