Tests for Asymmetry in Possibly Nonstationary Time Series Data

Tests for asymmetric adjustment in possibly nonstationary, nearly nonstationary, or stationary time series data are developed. The asymmetry is modeled 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 instrumental-variable estimators and are asymptotically normal or chi-squared regardless of stationarity/nonstationarity of data-generating processes. This is in contrast to the fact that the t tests and the Wald tests based on the ordinary least squares estimator (OLSE) are asymptotically normal and chi-squared, respectively, only under stationarity and are thus statistically invalid under nonstationarity. A Monte Carlo simulation shows that the proposed tests have stable sizes. Powers of the proposed tests against stationary 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 OLSE when data-generating processes are random walks. The proposed tests are applied to a monthly U.K. interest-rate dataset to find evidences for asymmetry in directions of adjustments as well as in amounts of adjustments.