I need to run several tests in R to make sure that the basic linear model assumptions hold for this time series OLS model. I'm very new to this, so I'm unsure in some cases of how to test for these, in others how to correct for them. Here's what I have so far:
Normality of residuals can be tested with an normal probability plot and histogram superimposing the normal curve; the correction, I believe, is removing outliers from the data.
Independence (lack of autocorrelation) can be tested for with a Durbin-Watson test or by examining a sample ACF plot. The correction is Newey-West or robust standard errors.
Heteroskedasticity can be tested for with a scatterplot with residuals on the y-axis and fitted values on the x-axis, and I should be able to observe a changing variance. The correction, I believe, is still also robust standard errors (i.e., the above correction should also fix this, right?).
Endogeneity: I'm not sure how to test for this, and the only correct I know of is using instrumental variables and 2-stage least squares. Is there another way to correct for this?
Multicollinearity: VIF test, and the cut-off point could be specified as something between 5 and 10. (I've been advised to use 10.) The correction is removing variables with high VIF's and rerunning the test until the remaining VIF's are satisfactory.
Stationarity: unit-root test. I'm still struggling to implement this in R, but I am aware of the "urca" package and am attempting to test it out. The correction is differencing the series and rerunning the test, most likely throwing out variables that aren't stationary after a second difference.
My questions, then, are:
How would I test for endogeneity, hopefully in R, and how could I fix it without using 2-stage least squares?
Is there another way to correct for heteroskedasticity, or will robust standard errors take care of it? To that point, is there another way to test for this other than a scatterplot?
Are there any errors in what I've written above?