I've been fitting ARMA-GARCH models in R and I've found that when I plot the ACF and PACF of the model residuals, the lags ($x$ axis) go up to and beyond two million. What does this mean? Is it wrong? Also, can one ignore lags that are 'just' above the significance level?
Edit: Here is the acf and pacf plots I'm talking about. Notice the scale of the x axis …
Best Answer
As concerns your first question, I would say that there is something wrong, unless you have billions of data points and the interval between each data point is very small. In any case, autocorrelation in residuals is generally synonym of misspecification in the model.
As for your second question, I would say that 'No', you cannot ignore lags that are just above the significance level. Otherwise, that would not be a significance level...
When ignoring important lags, you acknowledge that the data generating process that you use is statistically different from the true data generating process. Therefore, you introduce misspecification into your model.
Whether you are fine with that or not is completely up to you.