Tests for asymmetry in possibly nonstationary time series data

Tests for asymmetric adjustment in possibly nonstationary, nearly nonstatio nary, or stationary time series data are developed. The asymmetry is modele d by the momentum threshold autoregressive model of Enders and Granger and an extension of it. The tests are t-type tests and Wald tests based on inst rumental-variable estimators and are asymptotically normal or chi-squared r egardless of stationarity/nonstationarity of data-generating processes. Thi s is in contrast to the fact that the t rests and the Wald tests based on t he ordinary least squares estimator (OLSE) are asymptotically normal and ch i-squared, respectively, only under stationarity and are thus statistically invalid under nonstationarity. A Monte Carlo simulation shows that the pro posed tests have stable sizes. Powers of the proposed tests against station ary alternatives are comparable to those of the OLSE-based tests. The Monte Carlo study also shows that the new estimators are less biased than the OL SE when data-generating processes are random walks. The proposed tests are applied to a monthly U.K, interest-rate dataset to find evidences for asymm etry in directions of adjustments as well as in amounts of adjustments.