Take‑Home: Classifying Buy‑Now vs Wait Decisions in Housing Time Series

Context

You are given a monthly panel of regional housing and macro time series (e.g., price indices, mortgage rates, inventory, days‑on‑market, unemployment, CPI). The goal is to build a system that, for each region and month t, outputs a calibrated probability and a recommendation: buy now vs wait (i.e., buy within the next k months).

Task

Describe, at design level and with enough specificity to implement:

1. Target and horizon
   • Define the decision horizon k and a rigorous target label y_t for month t.
   • Clarify economic assumptions and edge cases (e.g., transaction costs, right‑censoring).
2. Data preprocessing
   • Panel alignment by region and month, handling multiple data vintages if applicable.
   • Missing‑value strategy, outliers, scaling, and seasonality/deflation adjustments.
3. Temporal feature engineering
   • Lags, rolling statistics, deltas (m/m, y/y), seasonality dummies, and interaction features.
   • Handling non‑stationarity (e.g., differencing, deflation, time‑weighted fitting).
4. Time‑aware validation
   • Train/validation/test splits that respect time.
   • Walk‑forward (rolling/expanding window) cross‑validation and hyperparameter tuning.
5. Models
   • Baselines and candidate models (e.g., logistic regression with time features, gradient boosting, sequence models).
   • Rationale for choices given data size, interpretability, and regime risk.
6. Metrics and decisioning
   • Probabilistic metrics (AUC, Brier, calibration) and cost‑sensitive objectives reflecting asymmetric risks.
   • Derive a thresholding rule tied to user costs/utilities.
7. Leakage controls
   • Methods to prevent look‑ahead bias and data leakage (including macro data release lags and revisions).
8. Concept drift and monitoring
   • How to detect, diagnose, and handle drift post‑deployment; retraining cadence.
9. User presentation
   • How to present a calibrated probability and recommendation to end users, including explanations and scenario analysis.