# Understanding ACF and PACF plots for model selection for AR(1) vs AR(2)

Good afternoon all,

I've got a model that models a time series and I am trying to decide which how the residuals are correlated. The first model, called $$m1$$ is models $$AR(1)$$ residuals and the second model models $$AR(2)$$ residuals called $$m2$$. I'm looking at the residual plots, ACF/PACF plots and also the AIC/BIC values of the two models to decide if $$m1$$ or $$m2$$ would a better model for the residuals. However upon closer inspection I cannot determine which one would be best as they are both very similar in the analysis and I lean more towards the AR(1) model since it is simpler. Are my assessments correct on this and am I understanding the ACF/PACF plots correctly?

ACF/PACF of $$m1$$ and $$m2$$

Analysis: There appears to be slightly less variability in the ACF/PACF for the $$m1$$ model. I'm also having some issues fully understanding these ACF/PACF plots.

Plots of the residuals of $$m1$$ and $$m2$$

Analysis: No apparent difference in the residuals between the $$m1$$ and $$m2$$ as they are almost identical.

AIC/BIC values

m1: -286.812/-274.2221

m2: -287.7302/-271.9928

Analysis: AIC slightly favors $$m2$$ and BIC slightly favors $$m1$$.

Thank you for the time.

• Sorry, that was my bad. Yes I did forget the minus sign and the interpretation's also been fixed. Thank you for catching that. Commented Mar 14, 2023 at 20:46