1 Intro and Data

The data set has 476 observations of the monthly beer production for a company

In this case study, we use the beer consumption data to compare various models introduced in this note.

2 Accuracy Mesurments

The accuracy measures of various exponential smoothing models based on the training data
ME RMSE MAE MPE MAPE MASE ACF1
SES -0.2462 21.2048 16.4166 -1.2298 10.4669 1.8672 0.0475
Holt Linear -0.1551 21.2750 16.5565 -1.1855 10.5554 1.8831 0.0462
Holt Add. Damped -0.6404 21.2525 16.5528 -1.5075 10.5708 1.8827 0.0523
Holt Exp. Damped 0.5354 21.2540 16.5266 -0.7460 10.5066 1.8797 0.0449
HW Add. -1.2113 7.4484 5.9235 -1.0260 3.8974 0.6737 -0.1628
HW Exp. -1.1396 7.3508 5.8890 -0.9429 3.8608 0.6698 -0.1801
HW Add. Damp -1.4477 7.5466 5.9679 -1.1691 3.9370 0.6788 -0.1476
HW Exp. Damp -0.6056 7.3051 5.8694 -0.5982 3.8574 0.6676 -0.1999

2.1 Model Testing

The above table shows that the HW additive seems to be the most appropriate.

Case study: Comparing various exponential smoothing models.

Case study: Comparing various exponential smoothing models.

We can see from the above accuracy table that HW’s linear trend with an additive seasonal model is the best of the eight smoothing models. This is consistent with the patterns in the original serial plot.

Since we train the model with the training data and identify the best model using both training and testing data. Both methods yield the same results. To use the model for real-forecast, we need to refit the model using the entire data to update the smoothing parameters in the final working model.

2.2 Model Accuracy

The accuracy measures of various exponential smoothing models based on the testing data
MSE MAPE
SES 880.6973 18.03311
Holt.Add 946.3989 19.33940
Holt.Add.Damp 880.4131 18.02812
Holt.Exp 945.3528 19.31625
HW.Add 438.2519 11.95899
HW.Exp 427.3942 12.03835
HW.Add.Damp 462.8816 12.52942
HW.Exp.Damp 410.0403 11.41884

We can see from the above accuracy table that HW’s linear trend with an additive seasonal model is the best of the eight smoothing models. This is consistent with the patterns in the original serial plot.

In the previous analysis, we train the model with the training data and identify the best model using both training and testing data. In real-forecast, we need to refit the model at the very end using the entire data to update the smoothing parameters in the final working model.

Estimated values of the smoothing parameters in Holt-Winters linear trend with additive seasonality
x
alpha 0.0032568
beta 0.0032562
gamma 0.0001013

3 Summarry

In summary, the updated values of the three smoothing parameters in the Holt-Winters linear trend and with additive seasonality using the entire data are given in the above table.