Describe two methods for generating prediction intervals

WHAT THIS TESTS: This question tests your practical knowledge of forecasting beyond just generating a single number. Interviewers want to see if you can quantify the uncertainty of a forecast, which is critical for business decisions like inventory management or capacity planning. It assesses whether you know both parametric (assumption-heavy) and non-parametric (simulation-based) approaches to creating these uncertainty bounds.

A GOOD ANSWER COVERS: Two distinct methods. First, the classic statistical approach based on an assumed distribution. This method assumes the forecast errors are uncorrelated and follow a normal distribution with a mean of zero. The prediction interval is calculated as the point forecast plus or minus a multiplier times the estimated standard deviation of the h-step forecast error (y_hat ± c * sigma_h). The multiplier 'c' depends on the desired probability; for a 95% interval, c is 1.96. This method is simple but relies on strong assumptions. Second, bootstrapping residuals. This is a simulation-based, non-parametric method that makes fewer assumptions. You collect the residuals from your model on the training data. Then, you generate many future sample paths by repeatedly sampling with replacement from these residuals and adding them to your point forecasts. This creates an empirical distribution of possible future values. The 2.5th and 97.5th percentiles of this simulated distribution form your 95% prediction interval. This is more robust if errors are not normally distributed.

COMMON WRONG ANSWERS: A major red flag is confusing prediction intervals with confidence intervals. A prediction interval is a range for a future data point, while a confidence interval is a range for an unobservable model parameter (like a regression coefficient). Another weak answer is only describing the normal distribution method without acknowledging its limitations or being unable to name a second, different approach. Simply saying "you add and subtract the standard error" is too simplistic and misses the nuance of the multiplier and the underlying assumptions about the error distribution.

LIKELY FOLLOW-UPS: "When would you choose bootstrapping over the normal distribution method?" (When residual diagnostics show errors are not normally distributed or are not homoscedastic). "How does the prediction interval change as you forecast further into the future?" (It gets wider because uncertainty accumulates over time; the standard deviation of the forecast distribution increases with the forecast horizon). "What are the key assumptions of the normal distribution method?" (Forecast errors are uncorrelated and normally distributed with a mean of zero).

ONE CONCRETE EXAMPLE: For a sales forecast of 1,000 units next month, a point forecast is just "1,000". A probabilistic forecast provides a range. Using the normal distribution method with an estimated forecast standard deviation of 50 units, the 95% prediction interval would be 1000 ± 1.96 * 50, which is [902, 1098]. This tells a stakeholder you are 95% confident the actual sales will fall between 902 and 1098 units, which is much more useful for inventory planning than the single point estimate.