Forecasting quarterly EUR/USD exchange rate
There are many methods to forecast exchange rates- look at the series of influential papers by Meese and Rogoff for a primer (https://scholar.harvard.edu/files/rogoff/files/51_jie1983.pdf).

To answer your particular question- what you describe seems to be driven by  multicollinearity. For instance, returns on stocks will be correlated with the inflation rate if they are nominal,  CAB and FA balance will be related to both the GDP growth rate as well as the interest rates etc. To test whether your results are susceptible to multicollinearity in the variables, try Variance Inflation Factor type tests.