TESTING FOR NONINVERTIBLE MODELS WITH APPLICATIONS

This article is concerned with testing for noninvertible time series models. For a stationary but noninvertible autoregressive moving average model, I Construct a derived process that is nonstationary but invertible with a nonstationary factor identical to the noninvertible factor of the original time series. I then propose a test procedure for testing noninvertibility using various unit-root test statistics available in the literature. The limiting distributions of the test statistics employed depend on the mean as well as the initial innovations of the original series. I also compare the performance of the proposed test procedure with that of other noninvertible tests available in the literature. For illustration, I apply the proposed test procedure to detect trend stationarity of two U.S. economic time series.