I'm trying to understand how ETS selects whether to use a damped model via information criteria (I'm not sure which of AIC, AICc or BIC are used).
I have a time series and I'm comparing two ETS models, one that sets
damped = TRUE and the other that sets
damped = FALSE. Visually, the model with
damped = FALSE provides a better fit by capturing the trend.
Yet by AIC, AICc and BIC, damped provides a much better fit. Why do these penalized likelihoods prefer the damped model instead of the undamped model?
ETS(M,A,N) Call: ets(y = daily_max, damped = FALSE) Smoothing parameters: alpha = 0.1162 beta = 0.0025 Initial states: l = 3.703 b = 0.4918 sigma: 0.2977 AIC AICc BIC 7703.744 7703.829 7726.542
ETS(M,Ad,N) Call: ets(y = daily_max, damped = TRUE) Smoothing parameters: alpha = 0.088 beta = 1e-04 phi = 0.8773 Initial states: l = 0.4713 b = 2.8166 sigma: 0.3013 AIC AICc BIC 7680.163 7680.283 7707.521