Forecasting quarterly EUR/USD exchange rate My aim is to forecast the one-quarter ahead EUR/USD exchange rate. I have constructed a regression model with the following as explanatory variables: exchange rate in the previous quarter, EUR/USD futures price, American and European GDP growth rate, inflation rate, return on stocks, interest rate on 3-month govt. securities, current account balance, net financial account balance and dummies for the inversion of EU and US yield curve. All the explanatory variables are at one-quarter lag. The input data file could be found here.

I am getting spurious results - all these variables are coming out to be insignificant but surprisingly the R^2 is more than 90%.

Is OLS not a good technique for forecasting exchange rates? If not, then which other techniques could be used?
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.