In recent years substantial numbers of econometric papers have addressed estimation and inference methods of the Threshold Auto Regression model. Threshold Auto regression model are able to capture asymmetric and nonlinear movement of variables. This paper explains the characteristics of threshold models and some different applications of these models and then, investigates the threshold auto regression models and momentum threshold auto regression models. Finally, presenting some examples of threshold models, we used the threshold co Integration test advanced by Enders and Siklos (2001) to investigate the asymmetric adjustment on long-run (PPP) in Iran between 1339 and 1390. Results prove PPP theory and imply that the adjustment process towards long run PPP is asymmetric.