I'm studying about exponential smoothing methods and something I still can not understand is the behavior of level and trend components when you increase and decrease level and trend smoothing parameters.
Let $\alpha_1$ and $\alpha_2$ be the smoothing parameter for the level and $\beta_1$ and $\beta_2$ the smoothing parameter for the trend. Given the following two examples, where the first is with $\alpha_1$ and $\beta_1$ and the second with $\alpha_2$ and $\beta_2$.
Is $\alpha_1>\alpha_2$ and $\beta_1>\beta_2$? If yes why and if not why?
I was testing various combinations of coefficients to try to identify a behavior in the components, but I could not come to some conclusion yet. I know that assigning larger values to the parameters means assigning more weight to the more recent observations, but it seems to me that at some point some distortion of the components may occur.