# Confusing Holt-Winters parameters

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

Are these parameters normal for holt-winters?

• You should probably mention you're using the forecast package. Also your third line is incomplete so your example doesn't run. Please give code that actually works. – Glen_b -Reinstate Monica Oct 28 '14 at 9:46

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.
All parameters, $\alpha$, $\beta$ and $\gamma$, have values between 0 and 1. In broad terms, a simple exponential smoothing model looks like this (though the idea also works for double and triple exponential smoothing):
$$\mathit{smoothed_t} = \color{blue}{\mathit{parameter}} \cdot \mathit{observation_t} + (\color{blue}{1 - \mathit{parameter}}) \cdot \mathit{smoothed_{t-1}}$$