A multivariate linear regression for explaining impacts of the predictors
To handle autocorrelation, you should try to "subtract it" from the series. In other words, using differentiation, de-seasonalization, and transformations you should try to subtract the impact of time on your time series data. Once you end up with a distribution that looks like white noise, then you can run your regression.

You can do it with an ARIMA model, simply add all the AR(), I(), and MA() components in the regression equation, and then ignore them when you evaluate the impact of other coefficients.