1. Definition

  • A point forecast is a single predicted value for a future observation.
  • It represents the model’s “best guess” without explicitly showing uncertainty.

Formally:

$\hat{y}_{t+h} \in \mathbb{R}$

where $\hat{y}_{t+h}$​ is the forecast for horizon $h$.

2. Examples

  • Weather: “Tomorrow’s temperature will be 25°C.”
  • Sales: “Expected demand next month = 1,200 units.”
  • Energy: “Forecasted load at 6 PM = 30 GW.”

3. How Point Forecasts Are Produced

  • Statistical models: ARIMA, ETS, linear regression → output mean or fitted value.
  • Machine learning models: random forest, gradient boosting, neural networks → output a numeric prediction.
  • Quantile regression (special case): produces a point forecast for a chosen quantile (e.g., median).

Most commonly, the point forecast corresponds to the expected value (mean):

$\hat{y}_{t+h} = E[Y_{t+h} \mid \text{past data}]$

4. Advantages

  • Simple & clear: easy to communicate (e.g., “GDP will grow by 2%”).
  • Useful when uncertainty is low or when only a single decision threshold is needed.

5. Limitations

  • Ignores uncertainty in outcomes.
  • Can be misleading if future variability is large (e.g., stock market, weather extremes).
  • In decision-making, often insufficient — you may need prediction intervals instead.

6. Evaluation

Point forecasts are evaluated with error metrics comparing forecast vs observed outcome:

  • MAE (Mean Absolute Error)
  • RMSE (Root Mean Squared Error)
  • MAPE (Mean Absolute Percentage Error)

7. Contrast

  • Point forecast: Single number (best guess).
  • Prediction interval: Range of likely values (e.g., 95% chance sales between 1,000–1,400).
  • Probabilistic forecast: Full probability distribution of outcomes.

Summary:
A point forecast is a single predicted value for a future observation — the model’s best guess, often the mean. It is simple and widely used, but it ignores uncertainty. For risk-sensitive decisions, prediction intervals or probabilistic forecasts are more informative.