Modifying the model to include a trend component

Earlier, we added a linear trend line to the data. If we wanted to incorporate a linear trend into the forecast as well, we can substitute A for the second parameter (trend parameter), which yields an "AAN" model (Holt's linear trend). This type of method allows exponential smoothing with a trend:

fit <- ets(x, model = "AAN")
summary(fit) 
> ETS(A,A,N) 
> 
> Call:
> ets(y = x, model = "AAN") 
> 
> Smoothing parameters:
> alpha = 0.0312 
> beta = 0.0312 
> 
> Initial states:
> l = 0.1641 
> b = -0.0021 
> 
> sigma: 0.0042
> 
> AIC AICc BIC 
> -108.5711 -104.1267 -106.0149 
> 
> Training set error measures:
> ME RMSE MAE MPE MAPE
> Training set -0.000290753 0.004157744 0.003574276 -0.2632899 2.40212
> MASE ACF1
> Training set 0.7709083 0.05003007

Plotting...