Describe two methods for generating prediction intervals or probabilistic forecasts

WHAT THIS TESTS: The interviewer wants to see if you understand that point forecasts alone hide risk. They are testing your ability to generate prediction intervals, distinguish parametric from empirical uncertainty quantification, and connect statistical output to business decision-making under uncertainty.

A GOOD ANSWER COVERS: Two distinct methods in this order. First, parametric analytical intervals. Assume forecast errors follow a distribution, typically normal, and compute the interval as the point forecast plus or minus a multiplier c times the estimated standard deviation of the h-step forecast distribution. For 95 percent coverage, c is 1.96; for 80 percent, c is 1.28. You must note that sigma-h is horizon-specific because forecast variance usually grows as h increases. Second, bootstrap or simulation-based intervals. Resample historical residuals with replacement, add them to the fitted values, simulate thousands of future sample paths, and extract empirical percentiles. This avoids normality assumptions and captures skewness or bounds naturally. A great candidate also contrasts them: parametric is fast and clean when normality holds; bootstrap is robust but computationally heavier. Finally, translate to stakeholders by framing intervals as scenario ranges, for example, a 95 percent interval means demand will fall between X and Y nineteen times out of twenty.

COMMON WRONG ANSWERS: Confusing confidence intervals with prediction intervals. Confidence intervals quantify uncertainty around a parameter estimate; prediction intervals quantify uncertainty around a future observation. Another red flag is assuming constant variance across all forecast horizons. A third is proposing to use the standard deviation of the raw time series rather than the standard deviation of the forecast errors.

LIKELY FOLLOW-UPS: How does the width of the interval change as the forecast horizon lengthens? What would you do if the residuals are heavily skewed or the variable is bounded below by zero? How would you explain a prediction interval to a CFO who only cares about worst-case inventory risk?

ONE CONCRETE EXAMPLE: Suppose your model forecasts next week sales at 1000 units with normally distributed errors. Using the parametric approach and an estimated h-step standard deviation of 150, the 95 percent prediction interval is roughly 1000 plus or minus 294, giving 706 to 1294 units. Alternatively, you bootstrap the last 104 weekly residuals, simulate 10000 future paths, and find the empirical 2.5th and 97.5th percentiles land at 720 and 1310. The slight asymmetry reveals right-skewed errors that the normal model smoothed over, which matters for stockout versus overstock risk.

Source: otexts.com, Forecasting: Principles and Practice (2nd ed), Section 3.5 Prediction intervals.