Exchange rate movements can significantly impact not only foreign trade, capital flows, and asset portfolio management, but also real economic activity. Therefore, the forecast of exchange rates has always been of great interest among academics, economic agents, and institutions. However, exchange rate series are essentially dynamic and nonlinear in nature and thus, forecasting exchange rates is a difficult task. On the other hand, deep learning models in solving time series forecasting tasks have been proposed in the last half-decade. But the number of formal comparative study in terms of exchange rate forecasting with deep learning models is quite limited. For this purpose, this study applies ten different models (Random Walk, Autoregressive Moving Average, Threshold Autoregression, Autoregressive Fractionally Integrated Moving Average, Support Vector Regression, Multilayer Perceptron, Recurrent Neural Network, Long Short Term Memory, Gated Recurrent Unit and Autoregressive Moving Average-Long Short Term Memory Hybrid Models) and two forecasting modes (recursive and rolling window) to predict three major exchange rate returnsnamely, the Canadian dollar, Australian dollar and British pound against the US Dollar in monthly terms. To evaluate the forecasting performances of the models, we used Model Confidence Set procedure as an advanced test. According to our results, the proposed hybrid model produced the best out-of-sample forecast performance in all samples, without exception.