Decomposition with a centred moving average: seasonal adjustment, forecasting, model critique
dairy
A dairy co-operative recorded milk solids collected (million kg) in one region each month from July 2020 (m=1) to June 2024 (m=48). Figure 1 shows the monthly series with its 2×12 centred moving average (CMA). A straight line was fitted to the CMA:
$T^=40.413+0.0361m$
Figure 2 shows the estimated monthly seasonal effects (million kg): Jul −8.78, Aug +2.10, Sep +13.93, Oct +19.69, Nov +18.16, Dec +9.72, Jan +5.35, Feb −0.89, Mar −3.26, Apr −10.34, May −21.25, Jun −24.44.
Collections in selected months (million kg):
| Season | Jul | Oct | Jan | May | Jun |
|---|---|---|---|---|---|
| 2020–21 | 32.7 | 56.8 | 47.1 | 19.0 | 17.1 |
| 2021–22 | 33.1 | 62.3 | 46.0 | 20.8 | 17.1 |
| 2022–23 | 31.5 | 59.4 | 46.1 | 20.4 | 16.6 |
| 2023–24 | 33.2 | 61.9 | 46.3 | 23.0 | 15.7 |
Line graph of monthly milk solids collected (million kg) for months 1 to 48 with the 2×12 centred moving average; collections swing from about 16 to 62 million kg each year, peaking in October–November and lowest in May–June, while the moving average is almost flat at about 40 to 42 million kg.
Bar chart of the twelve monthly seasonal effects (million kg) from July to June; positive bars from August to January peaking in October, negative bars from February to July with the lowest in May and June.Facts you may need
(a)
Use Figures 1 and 2 to describe the key features of the milk-solids series, using the model to support your answer.
(b)
Seasonally adjust the May 2024 and June 2024 collections and compare them with the trend. What might explain the result?
(c)
Forecast collections for October 2024 and January 2025.
(d)
Discuss TWO limitations of using this additive model to forecast the 2024–25 season, and suggest how one could be addressed.
