Tests for the order of integration against higher order integration

Abstract

Locally best invariant tests for the null hypothesis of I(p) against the alternative hypothesis of I(c), p < q, are developed for models with independent normal errors. The tests are semiparametrically extended for models with autocorrelated errors. The method is illustrated by two real data sets in terms of double unit roots. The proposed tests can be used for determining integration orders of nonstationary time series.