When the errors are distributed normally then OLS (easiest) = MLE (numerical solution)
When the variance of the errors change from observation to observation (over time in your case) you have:
If the change is autocorrelated then you have to use arch models:
Which mean at least two courses in undergrad econometrics (OLS and Time Series). A good start could be Introductory econometrics by Wooldridge.
This link could be very useful and easy to understand:
Said that you could find a least squares solution to a system by simply doing:
x = A\b (OLS)
Good luck
