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According to https://en.wikipedia.org/wiki/Box%E2%80%93Jenkins_method :

Statistical model checking by testing whether the estimated model conforms to the specifications of a stationary univariate process. In particular, the residuals should be independent of each other and constant in mean and variance over time. (Plotting the mean and variance of residuals over time and performing a Ljung–Box test or plotting autocorrelation and partial autocorrelation of the residuals are helpful to identify misspecification.) If the estimation is inadequate, we have to return to step one and attempt to build a better model.

I want to do that check on my model? What is considered the "estimated model"? The fitted values maybe?

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  • $\begingroup$ residuals of the fitted values is that? $\endgroup$
    – Clabis
    Nov 18, 2021 at 11:32
  • $\begingroup$ What do you think about my answer? If it is helpful and clear, you may accept it by clicking on the tick mark to the left. Otherwise, you may ask for further clarification. A helpful answer can also be upvoted by clicking on the upward-pointing arrow. This is how Cross Validated works. $\endgroup$ Jan 12, 2022 at 15:51

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For model diagnostics and assessment of the model's statistical adequacy, inspect its residuals as indicated in the quote. By definition, we have $y=\hat{y}+e$ where $y$ are the actual values, $\hat{y}$ are the fitted values and $e$ are the residuals. A model takes $y$ as input and produces $\hat{y}$ and $e$ as output. You should inspect $e$.

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