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I am working on a project whose goal is to build a linear regression model for a time series dataset. I was provided with a blueprint of all required analysis steps. This led me to wonder what is the optimal sequence for conducting these steps, and I would like to discuss it.

Steps in the provided tempate

  1. Plots and basic characteristics of variables (looking for outliers, variance, means etc)
  2. Testing stationarity
  3. Look at correlation (pair) plots
  4. Build initial model on all variables and check p-values for coefficients and $R^2$.
  5. Compute correlation matrix
  6. Find most important features with some method
  7. Build new model, with subset of features. Analyze adjusted R-squared, information criteria and F-statistics.
  8. Testing normality of residuals.
  9. Testing and removing autocorrelation.
  10. Testing and removing heteroscedascity.
  11. Test normality of residuals again (after corrections in steps 9 and 10).
  12. Test multicollinearity (VIF)
  13. Perform statistical test called RESET to test hypothesis about linearity of the model.
  14. Test catalysis effect
  15. Test coincidence effect
  16. Build final model and interpret results.

Note: Some of the methods are new to me yet, I need to read more about them - and I mean steps 13, 14 and 15.

My thoughts / questions so far

a. Step 5 should be moved into step 3 as it's just its numeric version.

b. Step 12 could also be merged with 3 and 5 and performed before fitting the model (at least the second model, the first built model can be built before that, just out of curiosity, even if there is a strong multicollinearity).

c. Steps 9 and 10 should IMO be performed earlier.

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