Design a time-series home-buy decision classifier

You are given monthly housing-market time series by region (e.g., price indices, mortgage rates, inventory, days-on-market, macro indicators). Frame this as a classification task to decide whether a buyer should purchase this month versus wait (or purchase within the next k months). Describe: how you would define the target label and decision horizon; data preprocessing and handling missing values; temporal feature engineering (lags, rolling statistics, deltas) and dealing with non-stationarity; time-based training/validation splits and walk-forward cross-validation; models you would try (e.g., logistic regression with time features, gradient boosting, sequence models) and why; evaluation metrics and cost-sensitive objectives reflecting asymmetric risks; methods to avoid look-ahead bias and leakage; approaches to detect and handle concept drift post-deployment; and how you would present a calibrated probability and recommendation to end users.