BFO 7010 Module 4 Written Assignment: Time Series Regression With Trend, Seasons and Weather Example

Weather Beats the Calendar: Regression Forecasts of Propane Deliveries

Student Name

MBA in Data Analytics, Thomas Edison State University

BFO-7010: Business Forecasting

Mentor Name

Month Day, Year

Weather Beats the Calendar: Regression Forecasts of Propane Deliveries

The Two Models

Model A explains gallons with a linear trend and eleven dummy variables for February through December, January serving as the base month. Model B replaces the dummies with heating degree days, the sum of the amounts by which each day's average temperature falls below 65 degrees Fahrenheit, a standard measure of heating demand. Hyndman and Athanasopoulos (2018) advise checking a regression's residuals for leftover autocorrelation before trusting its prediction intervals, and that check is built into the analysis below.

Part A: Interpreting the Coefficients

In Model A, deliveries rise by about 1,200 gallons a month after removing the seasonal pattern, and a July delivers about 418,500 fewer gallons than a January. In Model B, each additional heating degree day adds about 417 gallons, and the trend falls slightly to 1,100 gallons a month because some of what looked like trend in Model A was a run of colder winters. Both trend coefficients are many standard errors from zero.

Part B: Comparing Fit and Forecasts

Model B wins on every measure while using three parameters instead of thirteen. Calendar dummies assume each January needs the same fuel; heating degree days let a cold January need more, which is what happens. Both models beat the seasonal naive benchmark from Module 2, which had a test RMSE of 38.3; Hyndman and Koehler (2006) note that such scale-dependent comparisons are valid only on the same series, as here.

Part C: Ex Post and Ex Ante Forecasts

Model B's 24.5 RMSE uses 2024's actual heating degree days, an ex post forecast that could not have been made in advance. To forecast genuinely, Pinelands must supply future weather. Using 30-year normal heating degree days for each month, the ex ante forecast had an RMSE of 24.2, almost identical, because 2024's weather was close to normal. In a colder winter, the ex ante forecast would miss by the weather surprise: January 2024 had 1,022 heating degree days against a normal of 950, and the ex ante forecast of 635,800 gallons compared with an actual 618,200. If managers adjust the forecast for known events, such as a large new customer, Fildes and Goodwin (2007) suggest recording each reason so the adjustment can be evaluated later. The model is most useful for planning with scenarios, such as a winter 15 percent colder than normal, rather than for a single forecast.

Part D: Residual Diagnostics

Model B's residuals have a first-order autocorrelation of 0.36, so errors persist from one month to the next. Least squares estimates remain unbiased, but their standard errors are understated and the prediction intervals too narrow. The remedy, a regression with autocorrelated errors, is the dynamic regression of Module 8. The trend and weather model is the better choice now, with its intervals treated as optimistic.

Part E: Do the Month Dummies Add Anything?

A third model combined the trend, heating degree days and all eleven month dummies. Its adjusted R-squared, 0.981, is no better than Model B's, its AIC of 377.9 is worse, and an F-test of the eleven dummies together gives F = 0.61 with 11 and 46 degrees of freedom, far from significance. Once weather is in the model, the calendar adds nothing; the seasonal pattern is the weather pattern. Its 2024 test RMSE of 23.2 is a shade lower than Model B's, but one year is too little evidence to justify eleven extra parameters.

Refitting Model B on expanding windows and forecasting each year from 2021 to 2024 with normal weather gave an average RMSE of 32.7, against 42.0 for the seasonal naive benchmark over the same years. The weather model's advantage is largest in 2022, the cold winter, which is exactly where planners most need a better forecast.

References

Fildes, R., & Goodwin, P. (2007). Against your better judgment? How organizations can improve their use of management judgment in forecasting. Interfaces, 37(6), 570-576. https://doi.org/10.1287/inte.1070.0309

Hyndman, R. J., & Athanasopoulos, G. (2018). Forecasting: Principles and practice (2nd ed.). OTexts.

Hyndman, R. J., & Koehler, A. B. (2006). Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679-688. https://doi.org/10.1016/j.ijforecast.2006.03.001