I notice that when fitting exponential smoothing models with the
ets() function in the R
forecast package that a multiplicative trend is typically not detected if the growth rate is fairly strongly autoregressive. For example,
x <- cumprod(exp(arima.sim(model=list(ar=0.5), 500)*.01+.01)) ets(x, damped=F, allow.multiplicative.trend = T)
Will usually return a model with an additive trend. When growth rates are less autoregressive than a multiplicative trend is more likely to be detected.
What is the basic explanation for why
ets() will usually reject the multiplicative model? What would be another way to detect if a time series has an additive or multiplicative trend (taking into account that the series may also have seasonality and all the other things that