1. Example 16.7a Deseasonalizing: The Ratio-to-Moving-Averages Method

2. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.2a | 16.7 | 16.7b16.1a16.216.316.416.516.616.2a16.716.7b COCACOLA.XLS n We return to this data file that contains the sales history from 1986 to quarter 2 of 1996. n Is it possible to obtain the same forecast accuracy with the ratio-to-moving-averages method as we obtained with the Winters’ method?

3. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.2a | 16.7 | 16.7b16.1a16.216.316.416.516.616.2a16.716.7b Ratio-to-Moving-Averages Method n There are many varieties of sophisticated methods for deseasonalizing time series data but they are all variations of the ratio-to-moving-averages method. n This method is applicable when we believe that seasonality is multiplicative. n The goal is to find the seasonal indexes, which can then be used to deseasonalize the data. n The method is not meant for hand calculations and is straightforward to implement with StatPro.

4. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.2a | 16.7 | 16.7b16.1a16.216.316.416.516.616.2a16.716.7b Solution n The answer to the question posed earlier depends on which forecasting method we use to forecast the deseasonalized data. n The ratio-to-moving-averages method only provides a means for deseasonalizing the data and providing seasonal indexes. Beyond this, any method can be used to forecast the deseasonalized data, and some methods work better than others. n For this example, we will compare two methods: the moving averages method with a span of 4 quarters, and Holt’s exponential smoothing method optimized.

5. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.2a | 16.7 | 16.7b16.1a16.216.316.416.516.616.2a16.716.7b Solution -- continued n Because the deseasonalized data still has a a clear upward trend, we would expect Holt’s method to do well and we would expect the moving averages forecasts to lag behind the trend. n This is exactly what occurred. n To implement the latter method in StatPro, we proceed exactly as before, but this time select Holt’s method and be sure to check “Use this deseasonalizing method”. We get a large selection of optional charts.

6. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.2a | 16.7 | 16.7b16.1a16.216.316.416.516.616.2a16.716.7b Ration-to-Moving-Averages Output n This output shows the seasonal indexes from the ratio-to-moving-averages method. They are virtually identical to the indexes found using Winters’ method. n Here are the summary measures for forecast errors.

7. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.2a | 16.7 | 16.7b16.1a16.216.316.416.516.616.2a16.716.7b Ratio-to-Moving Averages Output

8. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.2a | 16.7 | 16.7b16.1a16.216.316.416.516.616.2a16.716.7b Forecast Plot of Deseasonalized Series n Here we see only the smooth upward trend with no seasonality, which Holt’s method is able to track very well.

9. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.2a | 16.7 | 16.7b16.1a16.216.316.416.516.616.2a16.716.7b The Results of Reseasonalizing

10. 16.116.1 | 16.1a | 16.2 | 16.3 | 16.4 | 16.5 | 16.6 | 16.2a | 16.7 | 16.7b16.1a16.216.316.416.516.616.2a16.716.7b Summary Measures n The summary measures of forecast errors below are quite comparable to those from Winters’ method. n The reason is that both arrive at virtually the same seasonal pattern.