Ridge regression and autocorrelation Im currently working with a strongley balanced data set. I have 15 countries over the period 1990-2017. My dependent variable is CO2 emissions. My independent variables are as follows, GDP per capita, total population, petroeleum prducts used and urban population as a % of total population. All variables are taken in log as I am following the STIRPAT framework. 
I had originally tested for my coefficients using fixed effects, however due to the problem of multicollinearrity I chose to use the ridge regression model. 
My issue now is, how do I test for the presence of heteroskedascity and autocorrelation? Are using OLS test applicable? If so, if the presence of autocorrelation is found, what are my options for correcting it?
 A: 
[H]ow do I test for the presence of heteroskedascity and autocorrelation?

You can use the common tests just as you would when evaluating a regression estimated by OLS. The fact that the model coefficients were estimated with $L_2$ penalty does not affect the testing procedure.

[I]f the prescence of autocorrelation is found, what are my options for correcting it?

You can use the common remedies such as modelling the error term explicitly as an ARMA (or AR or MA) process. This is trivial if estimation is done in two stages (ridge regression first followed by ARMA for the error term) but could be difficult to implement if you choose the more efficient simultaneous estimation. 
A: In order to omit heteroscedasticity you can use weighted regression, it should help you reduce this effect. If we talk about multicollinearity, you can use PCA before fitting your model. Then you will be able to extract important linear combinations of the variables that will not be related to each other. For autocorrelation, except standard econometrics method, maybe you can try RandomForest. Bagging methods can be very good for models where we are not able to remove autocorrelation (see Lopez de Prado - Advances in Financial Machine Learning)
