| Course | BFO-7010 Business Forecasting |
|---|---|
| Module | Module 6 |
| Paper type | Module 6 written assignment: exponential smoothing methods |
| Length | About 776 words, 5 pages |
| Format | APA 7 student paper |
| School | Thomas Edison State University |
| Program | MBA in Data Analytics |
| Updated | October 2026 |
Free sample paper for BFO 7010 Module 6
Four Smoothers, One Winter: Exponential Smoothing for Monthly Propane Deliveries
Student Name
MBA in Data Analytics, Thomas Edison State University
BFO-7010: Business Forecasting
Mentor Name
Month Day, Year
Four Smoothers, One Winter: Exponential Smoothing for Monthly Propane Deliveries
The Methods
Exponential smoothing forecasts with weighted averages of past observations, the weights shrinking geometrically with age. Simple exponential smoothing (SES) tracks only a level, governed by a smoothing parameter alpha between 0 and 1; a high alpha follows the latest value closely, a low one averages over many months. Holt's method adds a trend with its own parameter, beta. Holt-Winters adds a seasonal component with a third parameter, gamma, either added to the level (additive) or multiplied by it (multiplicative) (Hyndman & Athanasopoulos, 2018). Gardner (1985) traced how these methods spread through business forecasting because they are cheap to compute and update, and Hyndman et al. (2002) later placed them in a state space framework that gives them likelihoods and prediction intervals. Parameters here were chosen by minimizing the sum of squared one-step errors over the training months, with the seasonal methods started from the first year's averages.
Part A: Simple Exponential Smoothing and Holt's Method
SES chose an alpha of 0.98, which means it all but copies the previous month. That is the best a level-only method can do on a series that rises and falls by 400,000 gallons a year: chasing the last value is less wrong than averaging winter with summer. Its forecast for every month of 2024 is the December 2023 level, so it is reasonable in January and badly high by July.
Holt's method fails worse. Fitted to data whose last few months were climbing into winter, it ended 2023 with a level of about 578,000 gallons and a trend of nearly 100,000 gallons a month. Extended a year ahead, that trend forecasts 1.77 million gallons for December 2024, more than three times any month on record. The lesson is the one the textbook draws: a method's components must match the series' structure, and a trend method applied to seasonal data mistakes the seasonal climb for growth.
| Method | Fitted parameters | 2024 test RMSE, thousands of gallons |
|---|---|---|
| Simple exponential smoothing | alpha 0.98 | 226.6 |
| Holt's linear trend | alpha 0.98, steep trend | 915.5 |
Part B: Holt-Winters Additive and Multiplicative
Once the seasonal component is included, accuracy improves by a factor of seven over SES. The fitted parameters tell a story. The low alpha means the level is averaged over many months instead of chasing each one. The very low beta says the trend barely moves, consistent with the slow growth seen in the decomposition. The moderate gamma, around a third, lets the seasonal pattern adjust from year to year, partly absorbing the cold winter of 2022.
The two forms are almost tied on monthly error: the additive form has the lower RMSE and the multiplicative the lower MAE. They differ more on the annual total. The additive forecast falls about 155,000 gallons short of the 2024 total, while the multiplicative one lands within 4,000 gallons, because its winter peaks scale with the level and the level had risen. For a distributor that buys propane in annual contracts, the total matters, which favors the multiplicative form.
| Measure | Additive Holt-Winters | Multiplicative Holt-Winters |
|---|---|---|
| Alpha, beta, gamma | 0.20, 0.05, 0.35 | 0.10, 0.05, 0.30 |
| In-sample RMSE | 35.1 | 35.5 |
| 2024 test RMSE | 30.7 | 31.4 |
| 2024 test MAE | 27.3 | 26.2 |
| January 2024 forecast | 636.2 | 667.3 |
| 2024 total forecast | 4,644 | 4,803 |
| 2024 actual total | 4,799.3 | 4,799.3 |
Part C: Comparison With Earlier Models
Both Holt-Winters forms beat the benchmark, by about 20 percent, but neither beats the decomposition with drift or the weather regression on this test year. One reason is that Holt-Winters updates its seasonal indices month by month, so a cold or warm spell late in the training data tilts next year's pattern. The weather regression does not have that problem because it explains January's size with January's weather rather than with last January.
Holt-Winters still has two advantages for Pinelands. It needs no weather forecast, so it can run automatically each month, and in the state space form it produces prediction intervals without any extra modeling. A sensible use is as an automatic check on the regression: when the two disagree sharply, someone should look at why.
| Method | 2024 test RMSE |
|---|---|
| Seasonal naive benchmark | 38.3 |
| Decomposition, drift on adjusted series | 26.9 |
| Additive Holt-Winters | 30.7 |
| Multiplicative Holt-Winters | 31.4 |
| Trend and heating degree days regression | 24.5 |
Conclusion
On a strongly seasonal series, exponential smoothing works only once it has a seasonal component. Multiplicative Holt-Winters gives the most credible annual total of the smoothing methods, while the weather regression remains the most accurate month by month. The smoothing parameters themselves confirm what earlier modules found: a stable level, almost no trend change and a seasonal pattern that shifts a little each winter.
References
Gardner, E. S. (1985). Exponential smoothing: The state of the art. Journal of Forecasting, 4(1), 1-28. https://doi.org/10.1002/for.3980040103
Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: Principles and practice (2nd ed.). OTexts.
Hyndman, R. J., Koehler, A. B., Snyder, R. D., & Grose, S. (2002). A state space framework for automatic forecasting using exponential smoothing methods. International Journal of Forecasting, 18(3), 439-454. https://doi.org/10.1016/S0169-2070(01)00110-8
Reading the BFO 7010 Module 6 assignment instructions
This sample places exponential smoothing in Module 6. The syllabus lists six written assignments at 40 percent without pinning each to a module, so the slot is typical, not fixed. The textbook exercises behind this topic usually ask for SES and Holt's method on a non-seasonal series, then Holt-Winters on a seasonal one, with the smoothing parameters reported and interpreted and the forecasts compared on a test set or by cross-validation. Many versions also ask for the ETS model R selects automatically and for prediction intervals. The propane figures here are a composite series made for this page; your assignment will name the textbook data it wants.
How the BFO 7010 Module 6 example is put together
The methods section explains each smoothing method by the component it adds and cites the state space framework that gives the methods intervals. Part A reports SES and Holt's method, interprets the near-one alpha and explains, with the actual numbers, why Holt's trend runs away on seasonal data. Part B tabulates both Holt-Winters forms with their parameters, monthly errors and annual totals, reads each parameter in plain words and explains why the total favors the multiplicative form. Part C ranks every model built so far on the same test year and suggests a practical role for Holt-Winters beside the regression. The conclusion reads the fitted parameters back as facts about the business.
BFO 7010 Module 6 rubric: what earns full marks
Smoothing problems are marked as one of the six written assignments sharing 40 percent of the grade. Mentors check that each method is fitted correctly, that the parameters are reported and interpreted, that the right form is chosen for the series and that accuracy is compared on data the models did not see. Strong answers explain failures as well as successes, link the parameters to features of the data and compare the smoothing results with earlier models rather than in isolation. Because the syllabus stresses explaining how answers were reached, a sentence on how parameters were estimated and how the seasonal component was started earns credit too. Explaining a failed method, such as Holt's runaway trend, earns credit because it shows the student knows why components must match the data.
BFO 7010 Module 6 help: mistakes that cost marks
Students often apply Holt's trend method to seasonal data without comment, report parameters without saying what they mean, or choose between additive and multiplicative forms by error alone. Match the method to the series: plot it, and include a seasonal component when the pattern repeats. Read alpha, beta and gamma in words. Compare forms on monthly error and on any total the business plans around. Always include the benchmark from the simple methods module in your comparison. Ask for a free first sample run on your own Module 6 series. Report the smoothing parameters the software chose and say whether they make sense for gallons that swing with the winter.
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BFO 7010 Module 6 questions, answered
Where can I find a free BFO 7010 Module 6 sample paper?
The propane smoothing assignment above fits SES, Holt's method and both Holt-Winters forms, interprets each smoothing parameter and compares all of them on a hold-out year.
What does a high alpha mean in exponential smoothing?
The level follows the most recent observation closely; a low alpha averages over a longer stretch of history.
Why does Holt's method fail on seasonal data?
It reads the seasonal climb as a trend and extends it, producing forecasts that keep rising long after the season turns.
Additive or multiplicative Holt-Winters?
Additive when the seasonal swing stays roughly constant in size, multiplicative when it grows or shrinks with the level of the series.
How are smoothing parameters chosen?
Usually by minimizing the squared one-step forecast errors on the training data, or by maximizing the likelihood in the state space form.