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This study aims to construct continuous-time autoregressive (CAR) model and continuous-time GARCH (COGARCH) model from discrete time data of foreign exchange rate of United States Dollar (USD) versus Turkish Lira (TRY). These processes are solutions to stochastic differential equation Lévy-driven processes. We have shown that CAR(1) and COGARCH(1,1) processes are proper models to represent foreign exchange rate of USD and TRY for different periods of time February 2002- June 2010.