0.1 Case Study and Data Description

his is a dataset of the amount of beer produced which is taken in the year 1955-95 in New York. It contains 476 observations and the units are a count. this dataset is taken from Kagle, which is a website where many data miners share their ideas and publish their works.

The accuracy measures of various exponential smoothing models based on the training data
ME RMSE MAE MPE MAPE MASE ACF1
SES 0.1414 18.7918 14.8180 -1.0220 10.8510 1.5769 0.0376
Holt Linear -0.4934 19.2820 15.2353 -2.0349 11.3701 1.6213 0.4626
Holt Add. Damped 0.1761 18.7935 14.8371 -0.9821 10.8696 1.5789 0.0375
Holt Exp. Damped 0.2194 18.7941 14.8364 -0.9333 10.8658 1.5788 0.0366
HW Add. -0.1128 9.8822 7.4457 -0.4020 5.4666 0.7923 -0.1183
HW Exp. -0.1944 9.5649 7.1939 -0.5213 5.3084 0.7655 -0.0939
HW Add. Damp 0.5598 9.7863 7.4454 0.1368 5.4716 0.7923 -0.1031
HW Exp. Damp 0.3241 9.5304 7.2263 -0.1222 5.3289 0.7690 -0.1078

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

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

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. In order to use the model for real-forecast, we need to refit the model using the entire data to update the smoothing parameters in our final working model.

The accuracy measures of various exponential smoothing models based on the testing data
MSE MAPE
SES 525.8933 12.407904
Holt.Add 446.8495 11.435080
Holt.Add.Damp 525.9376 12.408569
Holt.Exp 525.4326 12.400720
HW.Add 164.4389 7.481143
HW.Exp 175.3590 7.586542
HW.Add.Damp 120.5422 6.398418
HW.Exp.Damp 139.1301 6.696372

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

In the previous analysis, we train the model with the training data and identify the best model using both our training and testing data.

Estimated values of the smoothing parameters in Holt-Winters linear trend with additive seasonality
x
alpha 0.0749061
beta 0.0060390
gamma 0.0834218

Next we need to refit the model at the very end using the entire data to update the smoothing parameters in the final working model. 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.