A Prediction Intervals and a Confidence Interval are related but serve different purposes:
-
Prediction Interval (
PI)- Estimates the range where a future single observation is expected to fall.
- Accounts for both the uncertainty in the model parameters and the natural variability/noise of the data.
- Example: “We predict that tomorrow’s temperature will be between 15°C and 20°C with 95% probability.”
-
Confidence Interval (
CI)- Estimates the uncertainty around an estimated parameter (like the mean of a population).
- Only reflects the uncertainty in the parameter estimate, not the variability of individual observations.
- Example: “We are 95% confident that the average temperature this month is between 16°C and 18°C.”
Key difference:
- PI is about where a new observation will fall.
- CI is about where a statistical estimate (like the mean) lies.
In time series forecasting, a 95% prediction interval tells you the likely range of the next actual value, while a 95% confidence interval would tell you the uncertainty around the expected forecasted mean.