This dissertation includes two chapters in the field of international finances about foreign exchange rate predictability and testing purchase power parity. In each chapter, we build the theory, methodology, and the empirical results to present the paper¡¦s construction. The first chapter, we studies whether the pure price inflation rate which is extracted from stock return can help us to test the relative of purchasing power parity in where Asian countries include Malaysia, Korea, Taiwan, Thailand, Hong Kong, and Singapore against the United States. The paper of Chowdhry et al. (2005) argue that relative PPP may not hold for the official price inflation rates which is constructed from consumer price indices, since relative price changes and other frictions cause price to be sticky. Thus, they use the Fisher equation and Fama-French three factors elaborately to build up a model on the nominal return of real risk-free asset to extract the pure price inflation rates. Their argument is supported in the case of Japan, Germany, the United States, and the United Kingdom. We are interested in the case of some Asian countries. So, this chapter, we extend the model and methodology of Chowdhry et al. (2005) to test the relative PPP for Asian countries. If our empirical evidence is firmly supported, it will be a strongly reconfirmed the elaborated idea of Chowdhry et al. (2005). In our study, the PPP rule is not supported for Asian countries since joint null hypothesis of a=0 and b=1 are rejected at all horizons except Taiwan at monthly horizon. The testing results by constrained seeming unrelated regression (SUR) and system equation in pooled data are similar to the tests of country-by-country. Therefore, we apply the methods of panel unite root from Im et al. (2003), Maddala and Wu (1999), and Pesaran (2007) to test the PPP doctrine, and it is strongly supported PPP for Asian countries. The second chapter, we extract the estimated data of pure price inflation by Chowdhry et al. (2005), and use the data to build up a nonlinear STR (smooth transition autoregressive) model by Granger and Teräsvirta (1993), then compare the performance of linear or nonlinear model of exchange rate predictability with random walk model in the United States, the United Kingdom, Japan, and Germany. This study has presented evidences that the extracted inflation rates offer a good predictability on the prediction of exchange rate for the United Kingdom and Germany. Those extracted data in which are calculated from the industry portfolio returns of stock market. The issue of series correlation in regression error does matter the estimated coefficients £]k, thus we estimate the simulation of Gaussian bootstrap distribution for testing variables with Newey West standard deviation in regression estimate. The empirical evidences show that the PPP doctrine affects the predictability performance of exchange rate change by the extracted inflation rates.