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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!

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    $\begingroup$ Can you add more detail such as what your data are, what the goal of analysis is, what tests you performed, and how you came to this conclusion? Also search for "Heteroscedasticity Autoregressive Consistent" sandwich standard errors and the R package sandwich. $\endgroup$ – AdamO Jun 7 '17 at 16:00
  • $\begingroup$ +AdamO So I am onto 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! $\endgroup$ – 박인호 Jun 7 '17 at 16:32
  • $\begingroup$ +AdamO and thx for the suggestions btw! $\endgroup$ – 박인호 Jun 7 '17 at 16:33
  • $\begingroup$ You should add this new information to the original post, please! $\endgroup$ – kjetil b halvorsen Jun 7 '17 at 17:11
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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.

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