Assuming I already have an existing linear regression model: $y(t) = a + bx(t) + e(t)$,
$a$ & $b$ are the constant coefficients
$e$ is the model residual error
$t$ denotes time
You've noticed that:
- There are trends in residuals and as a result the assumption of normality with constant variance is violated.
- There is "seasonality" in the model residuals showing repeating pattern in prediction errors over time (e.g. follows an annual cycle).
Question: How do we improve or adjust the model but without changing the constant coefficients?
This is only a hypothetical question. I am only looking for the approach that can be taken.