r - Forecasting Holt-Winters with and without trend -> Strange Results

Question

I am currently encountering a problem with the HoltWinters method implemented in the forecast package. If I use the method for some of my time series I have a larger error (SSE) when I use the Holt Winters with trend than without trend (Single Exponential Smoothing). As I understand, Holt Winters with trend should at least be as good as Holt Winters without trend. Can anybody explain this? I added an example below.

Best wishes,
Chris

library(forecast)

x = c(50,50,70,50,90,70,90,80,70,40,60,20,60,60,40,40,40,50,50,30,60,40,40,40,50,10,20,60,70, 60,60,80,70,80,90,80,70,30,30,80, 100,80,80,20,40,30,40,50,60,30,80, 100)  
mSES = HoltWinters(x, alpha = TRUE, beta = FALSE, gamma = FALSE)  
mHW = HoltWinters(x, alpha = TRUE, beta = TRUE, gamma = FALSE)

mSES$SSE  
mHW$SSE

Answer 1

不要将 alpha 或 beta 设置为 TRUE。如果 beta 设置为 FALSE，那么它将进行指数平滑，否则将输入作为特定参数值。所以 TRUE 被强制为 1。因此，与其让函数选择最小化 SSE 的参数，不如将它们显式设置为 1。