I have 5 independent variables and 1 dependent variables and I run up some codes in r and what I found was it didn't have any multi-colinearity but did have some heteroscedascity and auto-correlation as mentioned above. Is there any way I could correct these two simultaneously? The data are oil price analysis based on multiple linear regression whether the following factors are valid for influencing oil prices: 1) China Trade Volume 2) ANFCI (Adjusted National Financial Condition Index) 3) US oil supply 4) OECD stock. It turned out apart from ANFCI other factors was beyond 0.1% sig level. So we run ANOVA to decide whether ANFCI had problem of its own. It turns out it didn't. As for VIF analysis, it didn't have multicolinearity as well. I just need to correct heteroscedascity and autocorrelation!
As @AdamO hints in the comments, the typical way to deal with this is to use a heteroscedasticity and autocorrelation consistent sandwich estimator of the covariance matrix. The covariance matrix of your coefficients, estimated this way, can then be used for hypothesis tests. That is, the elements on the main diagonal that correspond to each coefficient can be used as a robust estimate of the coefficient's variance for a t-test.