The dissertation discusses an application of two statistical models to foreign exchange rate data and consists of two main parts. The first part is an application of the partial cointegration model developed by Johansen (1990) and uses the concept of weak exogeneity. While a direct application of the cointegration approach with many variables is not easy to handle, the partial model can reduce the number of the parameters to be estimated by identifying weakly exogenous variables. The method is illustrated utilizing a theoretical long-run model based on Dornbusch's sticky price model. The small country assumption is relaxed to that both countries are taken to be large. Furthermore the model is also extended to include a third country. The data set consists of monthly exchange rates, countries' money supplies, and GNPs. The three countries are Germany, Japan and the United States, thus giving a total of eight equations to be estimated. Three variables out of eight are identified as weakly exogenous variables and only five questions are estimated. Results show that there exist three cointegrating relations among the variables. One relation can be interpreted as long-run money market equilibrium while the other two relations, though considered to be long-run in nature, can not be interpreted in an economically meaningful way. Variance decomposition and impulse response analysis are conducted to investigate the dynamic of the system;In the second part of the dissertation a regime-switching stochastic volatility (RSV) model is applied to daily exchange rate data. The model is used to capture possible changing volatility of the exchange rate over time. The RSV model recommends itself since it is the more natural method to apply, as opposed to using ARCH and GARCH models. The main drawback however, is that it is the more complicated to implement. A Markov chain technique is used as an estimation method. By imposing interest rate parity, the relationship between exchange rate and foreign and domestic interest rate difference is also simultaneously examined. The results indicate that interest rate difference does not affect the level and the volatility of exchange rates. This finding supports the random walk theory of exchange rates. On the other hand two different regimes, a high-volatility regime and a low-volatility regime, are discovered and well modeled. The development of a forecasting model will be the subject for future studies.