Abstract:
Two new recursive trend adjustment methods are proposed and Lemma was constructed. The limit distributions of the unit root test statistics under the 4 recursive trend adjustment modes were deduced using the inferences from the Lemma,and the quantiles of the test statistics were obtained using Monte Carlo simulation. An empirical study was conducted on the trend adjustment test using a total of 1 000 observations of the closing price of the Shanghai Composite Index from January 2, 2019 to February 16, 2023.The theoretical research shows that as with existing adjustment methods, the newly adjusted variables no longer contain unknown parameters and can be used to construct unit root test statistics. The recursive trend-based adjustment of the test statistics converges to the generalised function of the Wiener process for large samples, but unlike the pre-existing distribution, the quantiles should be obtained through Monte Carlo simulation techniques. The simulation shows that though the first and the third test statistics increase while the second and the fourth test statistics decrease when the sample size increase, all quantiles converge in larger sample. Compared with the classical DF test, the recursive trend adjustment method can not only significantly reduce the estimation bias but also improve the test power while having a satisfactory test size. The empirical study shows that the recursive trend-adjusted test model can also obtain correct conclusions for both the series of log closed prices of SSE Composite Index and the series of yields.