Prediction cases: demand, pricing and the traps in each

CASE · Chapter 212 min readAsked at QuantCo, Two Sigma, Citadel, Point72

Assumes A method for open-ended research cases.

After this lesson you should be able to

  • Work a demand-forecasting case from target to baseline.
  • Recognise censoring and why it biases a demand model.
  • Handle a pricing case where the price itself is endogenous.

Prediction cases look like modelling exercises and are really data-definition exercises. In every one of them the interesting difficulty is that the thing you can measure is not the thing you want to predict — you observe sales rather than demand, and prices that were set in response to the very demand you are modelling.

Proposition 2.1

Sales are not demand

If you sold out, you do not know how much more you could have sold. Observed sales are censored at the inventory level, so a model fitted to them systematically underestimates demand exactly on the days demand was highest — which are the days the forecast matters.

Holds when

  • Flag stock-outs and treat those observations as censored rather than as observed demand.
  • A censored regression (Tobit) or a survival model handles it properly; dropping the days does not.
  • The bias is worst for the popular items, which is where the money is.

Example 2.2

Bike share

Forecast bike hires so a dispatcher can reposition bikes. Define the target and the baseline.

Show the worked solutionHide the worked solution

Worked solution

  1. Formula
    target=who decides what, and when?\text{target} = \text{who decides what, and when?}
  2. Substitute
    a dispatcher moving bikes within the hour\text{a dispatcher moving bikes within the hour}
  3. Solve
    Target: hires per station per hour, one to two hours ahead\textbf{Target: } \text{hires per station per hour, one to two hours ahead}
  4. Censoring: an empty station records zero hires, not zero demand\textbf{Censoring: } \text{an empty station records zero hires, not zero demand}
  5. Baseline: same station, same hour, same day of week, last four weeks\textbf{Baseline: } \text{same station, same hour, same day of week, last four weeks}
  6. Answer
    a strong seasonal baseline, and a censoring flag\text{a strong seasonal baseline, and a censoring flag}

Sanity check. The seasonal-naive baseline is formidable here: commuting patterns are extremely regular, so any model must beat "what happened at this station at this hour last Tuesday" before it has earned anything. Weather is the obvious first feature, and it is genuinely available as a forecast at prediction time.

FeatureAvailable at prediction time?Note
Hour, day of week, monthYesEncode cyclically, not as integers
Weather forecastYesUse the forecast, not the realisation
Actual weatherNoUsing it is look-ahead
Holidays and eventsYesKnown well in advance
Recent hires at this stationYes, with a lagMind the reporting delay
Hires at nearby stationsYesSpatial structure is usually the biggest gain
Table 2.3 · Features, and whether you will have them. The weather rows are the standard planted trap: training on realised weather and deploying on a forecast produces a model that works beautifully in the backtest and degrades the moment it is live.
050100012502500p × (100−p)PriceRevenue
Figure 2.4 · Why the pricing answer is a parabola. With demand falling linearly in price, revenue is a quadratic that peaks at the midpoint of the choke price. It is the first thing to write down in a pricing case — not because reality is linear, but because it gives you a number to be wrong about and a shape to reason with.

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Prediction cases: demand, pricing and the traps in each · QuantMax