week-11-notes: Space-Time Prediction

Bike Share Demand Forecasting with Panel Data & Temporal Lags

1 The Space-Time Challenge

Goal: Build a system that predicts demand in space and time

  • Panel data: Same stations observed over time
  • Temporal features: What happened last hour?
  • Space-time interaction: Different patterns by location and time

2 Panel Data

Definition: Data that follows the same units over multiple time periods

3 Binning Data into Time Intervals

4 Temporal Lags

Core idea: Past demand predicts future demand

  • lag1Hour: Short-term persistence (smooth demand changes)
  • lag3Hours: Medium-term trends (morning rush building)
  • lag12Hours: Half-day cycle (AM vs. PM patterns)
  • lag1day (24 hours): Daily periodicity (same time yesterday)

5 Creating the Space-Time Panel

The Challenge: Missing Observations Lag calculations break if rows are missing

Creating a Complete Panel

Calculate all possible combinations - Create every possible station-hour combination - Join to actual trip counts - Fill missing with 0

Joining Station Attributes - Station location, demographics from census - Join to panel

Adding Time-Varying Features - Weather changes hourly - Create time features

Final Panel Structure

  • Every station-hour combination exists
  • Trip counts (including zeros)
  • Station fixed attributes (location, demographics)
  • Time-varying features (weather, day of week, hour)
  • Temporal lags (lag1Hour, lag1day, etc.)

6 Temporal Validation

The Temporal Validation Problem

You CANNOT train on the future to predict the past!

7 Building Models

Model Progression Strategy

We’ll build 5 models, adding complexity:

  1. Baseline: Time + Weather only
  2. + Temporal lags: Add lag1Hour, lag1day
  3. + Spatial features: Add demographics, location
  4. + Station fixed effects: Control for station-specific baselines
  5. + Holiday effects: Account for Memorial Day weekend

Goal: See which features improve prediction accuracy

Evaluating Models: MAE

8 Space-Time Error Analysis

  • High MAE at high-volume stations might be acceptable
  • High MAE at low-volume stations might indicate systematic bias
  • Spatial patterns in errors suggest missing features
  • Temporal patterns suggest missing time dynamics

9 Policy Implications

Interpreting Results for Operations

For a bike rebalancing system:

  1. Prediction accuracy matters most at high-volume stations
    • Running out of bikes downtown causes more complaints
    • But: Is this equitable?
  2. Temporal patterns reveal operational windows
    • Rebalance during overnight hours (low demand)
    • Pre-position bikes before AM rush
  3. Spatial patterns suggest infrastructure gaps
    • Persistent errors in certain neighborhoods
    • Maybe add more stations? Increase capacity?

Next Steps to Improve

  1. More temporal features:
    • Precipitation forecast (not just current)
    • Event calendars (concerts, sports games)
    • School schedules
  2. More spatial features:
    • Points of interest (offices, restaurants, parks)
    • Transit service frequency
    • Bike lane connectivity
  3. Better model specification:
    • Interactions (e.g., weekend * hour)
    • Non-linear effects (splines for time of day)
    • Different models for different station types