I am trying to fit an ARMA model to the historical GBP/USD rates for the last 10 years. when I perform a one-step ahead prediction, the hit rate and other metrics come out fine. However, I am having trouble evaluating the performance of the fitted model's data.
When I plot the residuals from the fitted model and the fitted values vs the actual stationary data (i.e. I differenced it to make it stationary), the residuals closely match the stationary data, and the fitted values seem to represent the residuals. It's very confusing, especially with the good accuracy of the forecasts. Could there be a fundamental problem with the ARIMA function and the statsmodels.tsa library in python?
Any help would be appreciated. Thanks!