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Trying to understand when this issue is a problem:

If we fit a polynomial regression model, where the same feature x appears as x_squared and x_cubed, won't these three features all have correlated error terms?

Differently, would it be impermissible to include, in the same model, both wind direction (in degrees) and wind direction (in factors: NE, N, NW, etc...)? Won't these also have correlated error terms?

The following is a plot of my residuals as a function of time. Does the pattern suggest that there is some unaccounted for pattern in my linear model?

residuals over time

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