1
$\begingroup$

Assuming I already have an existing linear regression model: $y(t) = a + bx(t) + e(t)$,

where:

  • $a$ & $b$ 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.

$\endgroup$
1
$\begingroup$

If you know the length of the seasonal cycle in your residuals, you can fit an ARIMA model to the residuals, yielding a so-called regression with ARIMA errors. This will work only on residuals and leave your regression coefficient estimates for $a$ and $b$ as they are.

In R, you can do this using auto.arima in the forecast package. Feed your regressors into the xreg parameter.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.