# How come Exponential Smoothing without trend producing astonishing results when there is trend in the time series

I have a time series and a plot of it is presented below for consideration.

A linear trend was identified in the series both visually and using statistical tests such as Cox-Stuart and ManKendall. The statistical tests showed the presence of trend in the series. The ashtonishing thing happened when I modelled using Holt-Winters' exponential smoothing without trend/Beta with multiplicative and additive seosonality. The results that came out from both models were close to being the actual values. SMAPE of 0.011 and 0.009. I checked the residuals immediately to see if something has gone wrong but to my amusement there is one significant bar amongst the first 20 lags which can be due to chance. Now, what I am trying to figure out is the logic behind this phenomenon. I am new to the field of forecasting and If I do not make sense then please bear with me.

The ACF of exponential model without trend and additive seasonality is given below.

I have also tried other holt-winters' exponential models with all 3 parameters included but the residuals showed high autocorrelation and the SMAPE's were significantly low but not as low as the the SMAPE of the model mentioned above.

I would like an expert opinion on this please.

Thanks.

• Alpha=0.45, Gamma = 0.6. These were the parameter values in the exponential smoothing model that produced the above error and ACF plot. Does it mean anything?Is there an explanation of why such a behavior from exponential smoothing? – syebill May 25 '15 at 23:04
• I don't get what's astonishing here. By looking at the graph, I'd say any kind of smoothing should extract the trend. I can eyeball the trend. – Aksakal May 27 '15 at 13:05
• Statistics never ceases to astonish me – shadowtalker May 27 '15 at 15:43
• Hi Aksakal. I agree with what you have mentioned but I was of the understanding that if there is a trend in a time series then exponential smoothing should account for that which is the beta parameter. The result i got was without including the beta parameter and the accuracy of the result was ashtonishing as so far the time series I have worked with had not shown this. – syebill May 28 '15 at 10:46