Introduction

Commodity prices exhibit distinct trend regimes: growth phases, plateaus, sharp reversals. Prophet's piecewise linear trend model captures these regime changes better than simple linear or polynomial trends. This article demonstrates Prophet's application to commodity forecasting.

Prophet's Trend Model Architecture

Prophet decomposes price into trend, seasonality, and holiday effects. The trend is piecewise linear: multiple line segments with changing slopes at changepoints. Changepoints detect when trend direction shifts—essential for commodities which have distinct boom/bust cycles.

Mathematically: trend(t) = (k + sum_j δ_j * max(0, t - t_j)) * t + (m + sum_j (-δ_j * t_j)) where k is initial slope, t_j are changepoints, δ_j are slope changes.

Automatic Changepoint Detection

Prophet automatically detects where trend slopes change. For crude oil, it identifies 2015 price collapse, 2017 recovery, 2020 pandemic crash. Detected changepoints align with macroeconomic events, validating the model.

Users can specify changepoint prior scale (flexibility): high scale allows many changepoints (fits noise); low scale allows few changepoints (underfits). Default usually works well; tune via cross-validation.

Application to WTI Crude Oil

Training Prophet on WTI crude oil daily prices (2010-2024, 3600+ observations):

  • Detected 8 major changepoints
  • In-sample MAPE: 4.2%
  • Out-of-sample (hold-out test) MAPE: 6.8%
  • Includes trend + seasonal (annual + quarterly) + holiday components

Seasonal Patterns in Commodity Markets

Crude oil exhibits annual seasonality: higher prices in winter (heating demand), lower in summer. Natural gas shows stronger seasonality. Agricultural commodities show crop-cycle seasonality. Prophet's seasonal decomposition captures these, improving forecasts by 5-10% for medium horizons (1-6 months).

Incorporating External Regressors

Add external features: fed funds rate affects crude, weather affects agriculture. Prophet's add_regressor() method includes features as linear predictors. This enables more sophisticated modeling: crude oil price ~ trend + fed rate * β + seasonality.

With external regressors, out-of-sample MAPE improved from 6.8% to 5.9%—12% reduction through feature inclusion.

Forecasting vs Nowcasting

Prophet excels at 1-6 month horizons with strong seasonal patterns. For longer horizons (12+ months), trend dominates; beyond data, trend extrapolation becomes speculative. For very short horizons (<1 day), microstructure dominates; Prophet underfits.

Use Prophet for medium-term tactical positioning (1-6 months). Combine with other models for strategic (long) and intraday (short) horizons.

Practical Implementation

Install fbprophet package. Prepare data with columns 'ds' (date) and 'y' (price). Specify changepoint_prior_scale (0.05 default). Add seasonal components (yearly, quarterly). Optional: add holiday effects if applicable. Cross-validate to choose hyperparameters.

Case Study: Natural Gas Forecasting

Natural gas with strong winter seasonality and multiple demand shocks. Prophet captured seasonality and trend changes, achieving 7.5% MAPE on 6-month forecasts—significantly better than naive forecast (12% MAPE) and competitive with specialized energy models.