Tests for Asymmetry in Possibly Nonstationary Time Series Data
针对可能非平稳的时间序列数据，开发了基于工具变量估计的t检验和Wald检验，用于检测调整过程中的不对称性，并通过蒙特卡洛模拟和英国利率数据验证了方法的有效性。
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 ttests and the Wald tests based on the ordinary least squares estimator (OLSE) are asymptotically normal and chisquared, 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.