本项目由我国数据特征和国内外文献提炼出研究的理论问题：确定性趋势从低次到高次变化的单位根检验以及非线性非对称的单位根检验，其关键是检验统计量的渐近分布函数和有限样本性质及其随机趋势（有理论认为源于供给性冲击）的分解，由此为供给侧改革和经济新常态提供科学依据；将Philips等提出的中度偏离单位根扩展到带确定性趋势的中度偏离检验、将限于ADF框架的泡沫检验扩展到结构变化的泡沫检验，应用于我国金融数据，基于此评价市场运行；原创性地基于分布函数研究中度偏离、泡沫和（近）单位根过程的识别与转换，这一方向的关键是给出从中度偏离到（近）单位根的检验统计量和对应分布性质等，从而原创性地揭示中度偏离何时以及如何转换为单位根过程，将其应用于我国上证指数等是否从中度偏离转化为单位根，其结果直接作为是否干预（中度或泡沫）、什么时间干预（单位根转化为中度偏离）等问题的证据而体现出科学的现实意义，从而满足监管市场的迫切需要。

Based on Chinese data feature and current literature, this proposal extract theoretical problems: unit root tests with determinant trend breaks, say, from linear to quadratic trend, as well as unit root test with asymmetric exponential smooth transition auto-regression. So the target is to provide asymptotic distribution function and large sample properties, and we will apply the test to Chinese GDP and decompose its stochastic trend, which is an evidence for reforming on supply side and new normal for Chinese economy; We would extend moderate deviation (MD) process to MD with determinant trend, extend the bubble test based on ADF equations to bubble test with structural change in determinant trend, and apply the tests to Chinese financial data, so that we can conclude whether Chinese stock market (say) is weak efficient or not; This proposal will originally research the identification and transforming for MD, bubble and unit root process, the key problem in this direction is to develop a statistic and its asymptotic distribution (numerical distribution) for testing transformation from a MD process to a unit root process, applying the test(s) to stock markets. Results are evidence for whether to interpose stock market (MD or bubble), and the time for interposing (from unit root to MD or bubble).Thus, this original study has its scientific meaning for how to monitor capital markets.