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Learn through experiments

Forecast without seeing the future

How do smoothing and trend assumptions change a forecast?

Entering midway? Revisit Use a slope to improve a choice for the preceding worked example, or start here and use the explanation below.

1 · Try

Start with a concrete question

Original synthetic demand history begins 10,12,14,16. A held-out pair 18,20 is used only to evaluate the displayed predictions; it becomes exposed practice after inspection.

Try the initial inputs, then write a prediction before changing one setting. All calculations run locally on your CPU.

Go directly to the experiment · Review basic mathematics

2 · Predict

What do you expect?

Predict whether a longer average always improves a growing-series forecast.

3 · Experiment

Change one thing. Inspect what happens.

  1. Use the observed history to choose window and trend before reading errors.
  2. Compare a long and short average on this upward-trending sequence.
  3. Explain why repeatedly selecting the best settings on the visible pair is not independent evaluation.
Experiment inputs
Inputs
Your settingsMechanism
Calculation belowEvidence
Compare outcomes
Forecast next period17 units
Forecast second period19 units
Reserved-pair mean absolute error1 units

Compare the current results

Every bar starts at zero and uses the same numeric scale in this chart. The upper bound automatically adjusts to the largest current value (at least 1), so compare the numbers when changing inputs. Units and quantities come from each label; different kinds of quantity are not interchangeable. Displayed values are rounded to at most six significant digits.
020
  • Next prediction (units)17
    Next prediction (units): 17Horizontal bar from zero to 17, on the shared zero to 20 numeric axis.
  • Next actual (units)18
    Next actual (units): 18Horizontal bar from zero to 18, on the shared zero to 20 numeric axis.
  • Second prediction (units)19
    Second prediction (units): 19Horizontal bar from zero to 19, on the shared zero to 20 numeric axis.
  • Second actual (units)20
    Second actual (units): 20Horizontal bar from zero to 20, on the shared zero to 20 numeric axis.

Follow the calculation

  1. Observed history only: [10, 12, 14, 16].
  2. Recent 2-period mean = (14 + 16)/2 = 15.
  3. Forecasts = mean + horizon × trend: 17, 19.
  4. Held-out authored outcomes [18,20]; absolute errors [1, 1].

Choose a forecast before revealing evaluation outcomes. Repeated tuning on this visible pair turns it into practice, not an untouched forecast test.

Captures keep your inputs, prediction and observation. Results are recalculated from those inputs. Resetting inputs keeps your captures and challenge history.

4 · Understand

Explain the mechanism

Forecast without seeing the future

Original synthetic demand history begins 10,12,14,16. A held-out pair 18,20 is used only to evaluate the displayed predictions; it becomes exposed practice after inspection.

Predict before changing inputs

Predict whether a longer average always improves a growing-series forecast.

Understand the mechanism

A trailing average smooths variation but lags growth. With window 2 the mean of 14 and 16 is 15.

Adding assumed trend 2 per horizon predicts 17 and 19; errors against 18 and 20 are both 1. Mean absolute error is 1.

A backtest applies a forecasting rule to later observations that were not inputs to the forecast. Once used for tuning they are development evidence.

Calculate it yourself

Forecast at horizon h = mean of last k observed values + h × assumed trend; MAE = mean absolute forecast error.

Guided investigation

  1. Use the observed history to choose window and trend before reading errors.

  2. Compare a long and short average on this upward-trending sequence.

  3. Explain why repeatedly selecting the best settings on the visible pair is not independent evaluation.

Assumptions and limitations

  • Six invented values and a visible evaluation pair cannot establish general forecasting reliability.

  • Seasonality, shocks and prediction intervals are omitted; future trend is assumed, not estimated.

Further investigations

High school: Forecast a fictional sequence and explain one assumption.

College: Implement rolling-origin evaluation with a naive last-value baseline.

Working professionals: Write a demand forecast report that separates tuning data and future monitoring.

5 · Apply

Try a fresh case

Predictions are 8,12,16 and actuals are 10,11,19. What is mean absolute error?

This is a public practice check. Retries support learning; matching a number does not certify independent proficiency.

Take the investigation further

Choose any extension. These are project prompts for you to carry out; they are not automatically assessed.

School investigation

Forecast a fictional sequence and explain one assumption.

College investigation

Implement rolling-origin evaluation with a naive last-value baseline.

Workplace investigation

Write a demand forecast report that separates tuning data and future monitoring.

6 · Continue

Keep the evidence, choose your next step

Completion records your own decision that you have worked through this investigation. Practice checks and independent project evidence are separate.