This study investigates the behavior of the stock sectors indices for the Taiwan stock market for the period from 2003 to 2011.Select the Taiwan Weighted Stock Index, financial stocks, and 14 files of the financial holding stock index for the study the subject. Using traditional liner unit root and unconstrained two-regime threshold autoregressive (TAR) model with a unit root developed by Caner and Hansen (2001). Our main findings is that the Taiwan stock exchange capitalization weighted stock index (TAIEX) is a non-linear stationary series and Taiwan stock market prices do not follow random walks.