Q, DW and Dicky fuller Unit Root tests: all test the ACF of residual (not of the fitted model) to decide the model passes (is acceptable) as a forecaster or not.
Dickey Fuller: the smaller the values the better then model, if t
Error measures (RMSE, SSE, RSS, MAE): after checking that all models are acceptable, use these measures to check which model is best.
Q is more definitive than DW: no indecisive values in Q test. Use Q for your project!
SARIMA ~ Decomposition ~ Winters
Random Walk: use Differenced ARIMA for it.
ACF and PACF:
To detect seasonality: use ACF (not PACF), if there is a season of size x, ACF drops quickly then re-emerges quickly from the negative side of lag axes (wave shape).
ARIMA: Can ACF & PACF both fall quickly: usually only one of them falls quickly and the other shows spikes, indicating AR or MA.
If ACF or PACF are dropping slow: try increasing p,d,or q: AR, MA, or Difference.
If you have a regression of 1 dependent and multiple independent variables, and you found a correlation between 2 independent variables – This is called Multicollinearity:
1. If between Vt with Xt, you can remove one of them. This is dimensionality reduction.
2. If between Xt and X(t-1) then you should keep both, this means different terms in ARIMA.
Multiplicative vs additive Winters: When to choose each: The rule of thumb is use Multiplicative. We use Additive if we found the variance is not stable.
For different cyclicities: use different CI seasonal indices and multiply them. So [CI of dayOfWeek] x [CI of dayOfMonth].
Or Add dummy variables to the regression representing the seasonality, if their coefficient is too small (check H0) you can discard them.