Random Forest for Time Series

A Random Forest is not inherently a time-series model (like ARIMA or SARIMA), but it can be adapted for forecasting by converting the series into a supervised learning problem.

How to apply Random Forest to time series:

Feature Engineering

• Create lag features (e.g., $y_{t-1},y_{t-2},...,y_{t-k}$).
• Add rolling window statistics (mean, std, min, max).
• Include calendar/time features (day of week, month, seasonality indicators).
• Incorporate exogenous variables if available (weather, prices, events).

Training

• Each tree in the Random Forest learns patterns from these lagged and engineered features.
• Predictions are aggregated across trees (mean for regression).

Forecasting strategies

• Iteration: One-step ahead forecasting: Predict $y_{t+1}$ using features up to $t$.
• Recursive forecasting: Use the model’s own predictions as inputs for subsequent steps (risk of error accumulation).
• Direct forecasting: Train separate models for each horizon (e.g., $y_{t+1}$, $y_{t+2}$).

Advantages

• Captures non-linear relationships and interactions.
• Handles missing values and outliers relatively well.
• Can incorporate external covariates easily.

Limitations

• Does not naturally model time dependence like ARIMA/SARIMA.
• Recursive forecasts can accumulate errors (use Prediction Intervals).
  • How are accumulations of errors handled?
• Needs careful feature engineering to capture seasonality/trends.

When to use Random Forest for time series?

• When the series has complex, non-linear dynamics.
• When external features are strong drivers of the target variable.
• When interpretability of variable importance is valuable.

Related:

• ARIMA vs Random Forest in Time Series
• Time Series Forecasting