Solved – Confusing Holt-Winters parameters

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I have got a model for forecasting using holt-winters. However the parameters confuse me…
The parameters show that there is no trend or seasonality even though there is definite trend and seasonality in the data, the forecasts also match the pattern of the data so the parameters really do not make sense.

M<-matrix(c("08Q1", "08Q2", "08Q3", "08Q4", "09Q1", "09Q2", "09Q3", "09Q4", "10Q1", "10Q2", "10Q3", "10Q4", "11Q1", "11Q2", "11Q3", "11Q4", "12Q1", "12Q2", "12Q3", "12Q4", "13Q1", "13Q2", "13Q3", "13Q4", "14Q1", "14Q2", "14Q3",  5403.676,  6773.505,  7231.117,  7835.552,  5236.710, 5526.619,  6555.782, 11464.727,  7210.069,  7501.610,  8670.903, 10872.935,  8209.023,  8153.393, 10196.448, 13244.502,  8356.733, 10188.442, 10601.322, 12617.821, 11786.526, 10044.987, 11006.005, 15101.946, 10992.273, 11421.189, 10731.312),ncol=2,byrow=FALSE) Nu <- M[, length(M[1,])]  Nu <- ts(Nu, deltat=1/4, start = c(8,1)) N<-Nu HWMb <- ets(N, model = "MAM", damped = FALSE, opt.crit = "lik", ic="aic", lower = c(0.001, 0.001, 0.001, 0.001),              upper = c(0.999, 0.999, 0.999, 0.999), bounds = "admissible", restrict = FALSE)   HWMb Smoothing parameters: alpha = 0.0183  beta  = 0.0056  gamma = 0.0027

This shows the time series with the forecasts where you can see definite seasonality and trend

full data

Are these parameters normal for holt-winters?

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Best Answer

The small values for $beta$ and $gamma$ show that the trend and seasonality do not change much over time. They do not tell you that there is no trend or seasonality.

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