In recent years, there has been an increasing interest in the study of the nonlinear properties of macroeconomic and financial time series. In macroeconomics, the study of nonlinearity is based on an intuitive assumption that both the nature of the structural shocks hitting the economy and the dynamic properties of the economy might have changed. Using conventional econometric tests implies that the time series often contain unit roots and are due to the nonstationarity I(1). Some of these results contradict economic theories. Also, there is always an uncertainty about shifts in the persistence of a time series, such as shifts from stationarity I(0) to nonstationarity I(1) or vice versa. This thesis has attempted to investigate the nonlinear model and generalized stochastic unit root (GSTUR) using Bayesian analysis and MCMC numerical methods on the TEDPIX time series. Besides, a comparison between the nonlinear GSTUR model and the linear RW model can be achieved via the Bayes factors, which is not available in the classical framework.Using the NSE, RNE and CD, in this paper we investigate the MCMC algorithm and with sensitivity analysis on the prior parameters values, the sensitivity of results to changes in parameter values is investigated. Also the structural characteristics and parameters of distributions is checked and no significant Autocorrelated, with long lags, and the posterior data were fitted with the expected distributions, have been investigated. Implementation of the model with 48 models GSTUR, it was observed that the increase in p has little effect on improving the model. In all cases, the Models without the constant and regression not prefer to RW model, and compare the Bayes factor, the RW model is supported. But in all other types of GSTUR models class, these models are preferred to RW model. The results suggest that there is evidence of nonlinearity in TEDPIX time series and with a 99% probability it has a trend stationarity.