In this thesis, we study the unit root tests which includes the ADF, PP and KPSS tests, the long memory tests such as the R/S and GPH tests, and the applications of these methods in high frequency financial data analysis. The software SPLUS was adopted to analyze data and correction of the SPLUS program in unit tests are also proposed. To apply these two test methods in high frequency data, we quoted the library, HFlibrary designed by Yan and Zivot in 2003 for preliminary data analysis and propose a new library HFanalysis, which can be used in correcting high frequency data (excluding N.A. value, sorting transactions and retrieve a certain time of transactions), obtaining equi-distanced time intervals and testing for unit root and long memory properties. In additions, we apply this proposed library to simulate the power of traditional unit root methods such as the ADF test and long memory test method such as the R/S and to perform an empirical study. Finally, we explore the power of the ADF for testing data simulated from a threshold unit root model and simulate the percentiles of the null distribution of the following threshold unit root tests: WALD, LM, LR and W£f.