KPSS Test and Model Misspecifications

The KPSS test is very popular and used extensively by practitioners. The test considers two models under the null: stationarity around a deterministic level or around a deterministic trend. There is no study, as far as we know, on the statistical properties of the test when the wrong model is used. This paper endeavours to fill this gap. We found, using simulation, that choosing a deterministic trend when a deterministic level is true does not affect significantly the properties of the test. But, choosing a deterministic level when a deterministic trend is true lead to extreme over-rejection of the null. These results are obtained for i:i:d and autocorrelated errors.