Research on Recursive Trend Adjustment and Power Enhancement for Unit Root Test

Two new recursive trend adjustment methods were proposed, and the lemma was constructed. The limit distributions of the unit root test statistics under the 4 recursive trend adjustment modes were deduced with the inferences from the lemma, and the quantiles of the test statistics were obtained with 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 method. The simulation shows that though the first and third test statistics increase while the second and fourth test statistics decrease when the sample size increases, but all quantiles show a convergence trend. 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 results indicate that the recursive trend adjustment test model can obtain correct test conclusions for both the logarithmic closing price series and the yield series of the Shanghai composite index.