Making a forecast and writing the conclusion

How a forecast is built

• A forecast under the additive model has two parts:

$$\text{forecast} = \text{projected trend} + \text{seasonal effect}$$

• Step 1 — Project the trend forward. Extend the trend beyond the end of the data, usually by continuing its recent rate of change.
• Step 2 — Add the seasonal effect for the quarter or month being forecast.
• Step 3 — State the forecast in context, with units and the period it refers to.

Worked structure

• If the trend is rising by about 1 800 units per quarter, the last trend value is 52 000, and you are forecasting two quarters ahead into a quarter whose seasonal effect is $-4\,600$:

$$\text{projected trend} = 52\,000 + 2 \times 1\,800 = 55\,600$$

$$\text{forecast} = 55\,600 + (-4\,600) = 51\,000$$

• Do not forget the seasonal effect. A forecast that is just the projected trend has ignored the strongest short-term pattern in the data, and it is a common way to lose marks.

Every forecast rests on assumptions

• Stating these is required for Merit and developed for Excellence. A forecast assumes:
  • The trend continues at its recent rate.
  • The seasonal pattern stays the same size and shape.
  • No new events or shocks occur.
  • The underlying situation does not change — no new competitor, policy change, or structural shift.
• Say these explicitly, in the context of your data. Not "I assume the trend continues", but "this forecast assumes visitor numbers keep growing at the recent rate, which requires airline capacity on these routes to continue expanding."

How far ahead can you forecast?

• Reliability falls sharply with distance. One period ahead is reasonable; four is speculative; ten is not a forecast at all.
• Two reasons, both worth stating:
  • Errors compound. A small error in the trend rate multiplies with each period projected.
  • The chance of a change grows. The further out you go, the more likely something disrupts the pattern.
• The moving average makes this worse. Because trend values do not exist for the last few periods, you are already extrapolating before you start.

Judging your forecast

• Compare it with recent actual values. If your forecast for next Q1 is far from the last two Q1 figures, check your arithmetic.
• Ask whether it is plausible in context. A forecast implying a business will double in a year, or that arrivals will exceed the capacity of the airport, is telling you something is wrong.
• Give a range where you can. Saying the forecast is "about 51 000, though the irregular variation in this series has typically been around ±3 000, so a value between roughly 48 000 and 54 000 would not be surprising" is far stronger than a single number.

Writing the conclusion

• A conclusion that scores well does five things:

  • Answers the original question directly.
  • Summarises the trend with values.
  • Summarises the seasonal pattern with values and its contextual explanation.
  • States the forecast, with its assumptions and limitations.
  • Reflects on the investigation — what the model does and does not capture, other variables that would help, what you would do differently.

• The reflection is where Excellence lives. Useful things to raise:

  • Other variables that would improve the analysis — weather data for a tourism series, interest rates for a housing series, exchange rates for an export series.
  • Whether the additive model was adequate, with evidence.
  • Whether the data set was long enough — you need several complete cycles.
  • How the data were collected and whether definitions changed over the period.