However when fitting pairs of ARIMA and ETS equivalents in R I sometimes get different results. For example, compare forecasts from ARIMA(0,2,2) and ETS(AAN):
#Simulate random walk n <- 100 x <- cumsum(rnorm(n)) #Fit models arimafit <- Arima(x, order=c(0,2,2), include.constant = FALSE) etsfit <- ets(x ,"AAN", damped = FALSE) #Plot results plot(x, type = "l", xlim = c(0, n + (n/5))) lines(c(rep(NA, n), forecast(arimafit, h = n/5)$mean), col = "red") lines(c(rep(NA, n), forecast(etstrend, h = n/5)$mean), col = "blue")
I understand that this equivalence is conditional - ie the models can yield identical results given certain coefficient values. I am looking to understand what conditions result in more similar ETS/ARIMA forecasts and what conditions lead to divergence.