If we have a time series of returns and two time series of indicators, how would we test the use of these indicators if they are autocorrelated or nonstationary (VAR Models dont produce significant results).
The classical assumptions of linear regression are that the errors are uncorrelated and the variance of errors is constant (homoskedastic). So regress the returns against the indicators and test for autocorrelation and heteroskedasticity in the errors. If you don't observe any, then there's no issue with conventional hypothesis testing. If you do, use White or Newey-West standard errors (standard in most statistical packages), as appropriate, to compute new t-statistics, then proceed with hypothesis testing.