Forecast Reconciliation and Conformal Prediction for Time Series Data

Abstract

Forecast reconciliation ensures forecasts of time series in a hierarchy adhere to aggregation constraints, enabling aligned decision making. While forecast reconciliation can enhance overall accuracy in hierarchical or grouped structures, the most substantial improvements occur in series with initially poor-performing base forecasts. Here, we propose two categories of forecast reconciliation methods that incorporate time series selection based on out-of-sample and in-sample information, respectively. These methods keep “poor” base forecasts unused in forming reconciled forecasts to enhance forecast reconciliation.

Conformal prediction is a powerful and flexible tool for uncertainty quantification. However, the data exchangeability assumption is often violated for time series data. We propose the Autocorrelated Multi-step Conformal Prediction (AcMCP) method, which effectively incorporates autocorrelations in multi-step forecast errors, resulting in more statistically efficient prediction intervals. This method ensures theoretical long-run coverage guarantees for multi-step prediction intervals, though we note that increased forecasting horizons may exacerbate deviations from the target coverage, particularly in the context of limited sample sizes.