My residuals are autocorrelated. Will this be a problem if I want to use the time series to do forecasting?
If your residuals are autocorrelated then this means that there are systematic movements in your time series which your ARMA model has failed to capture. In that sense, forecasts are a risky affair. I know that parsimonious models are usually preferred by researchers but one has to at least make sure that the residuals are white noise in order to have a valid model, even if this means that the AR or MA order have to be increased by a bit.
Auto-correlation is not a problem for forecasting, so long as you take it into account. Ideally, you should add an allowance for auto-correlated error terms into your underlying model (whatever that is), and re-fit, to get simultaneous estimates of all your model parameters, including the estimated auto-correlation in error terms. Your forecast method should then incorporate the estimated auto-correlation.
If you have positive auto-correlation then your forecasts will predict higher values following outcomes that were higher than expected, and lower values following outcomes that were lower than expected. Contrarily, if you have negative auto-correlation, then your forecasts will predict lower values following outcomes that were higher than expected, and higher values following outcomes that were lower than expected.