Recursive mean adjustment and tests for nonstationarities

Recursive mean adjustment of Shin and So [Journal of Time Series Analysis 22 (2001) 595] and So and Shin (Statistics and Probability Letters 43 (1999) 65] is considered for inference on nonstationarities. The approach is shown to be versatile in that it can be applied to a wide class of tests for nonstationarities such as testing unit roots in nonlinear time series models, testing cointegrations, testing double unit roots, and testing seasonal unit roots. In all of the testing problems, recursive mean adjustment gives us tests with substantially higher powers than existing tests based on the ordinary mean adjustment.