# Understanding Intuition for ETS Damping Selection via AIC/BIC

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.

Undamped:

Damped:

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?

Undamped:

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


Damped:

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


The AIC and AICc are optimal for one-step forecasting. Over the course of your historical data, the damped model would do reasonably well, with the local trend sometimes heading up and sometimes heading down. If you think the trend near the end of the series will continue into the forecast period, then just set damped=FALSE.