Prediction-powered inference for time series across space

2026-10-06

AI Summary

This study addresses the challenge of prediction bias caused by short labeled sequences in spatiotemporal data, where conventional methods struggle with temporal dependence and heteroscedasticity. To overcome these limitations, this work pioneers the extension of Prediction-Powered Inference (PPI) to non-i.i.d. spatiotemporal settings, thereby relaxing the restrictive independent and identically distributed assumption. The proposed framework integrates PPI with heteroscedasticity and autocorrelation consistent (HAC) estimation and machine learning imputation techniques, effectively leveraging long-term unlabeled covariates for robust modeling. By doing so, it yields unbiased estimates and valid confidence intervals for each spatial location. Empirical results demonstrate that the method significantly outperforms existing baselines while preserving statistical rigor, enabling highly reliable estimation of future expected values.

Abstract

The following motif is common in spatiotemporal settings: we have a sequence of covariate and label pairs observed for a relatively short, recent time period. We have access to unlabeled covariates over a longer time period. Data is observed over many spatial locations. For instance, crop yield might be observed over a large geographical area for recent years, but weather data (which is informative about crop yield) is available for a much longer period. The goal is to estimate, at each spatial location, the expected label (e.g., crop yield) in the future and provide a valid confidence interval for this value. The observed time period alone is too short for reliable estimates. Imputing missing labels with machine learning can cause substantial bias. Prediction-powered inference (PPI) can correct for this bias, but it relies on an i.i.d. assumption that breaks under our expected temporal dependencies. Heteroskedasticity and autocorrelation consistent (HAC) procedures account for temporal correlation, but have not been adapted to cases where some labels are imputed. We provide reliable point estimates and confidence intervals given: short labeled time series (across spatial locations), a longer unlabeled time series, and an imperfect predictor of labels given covariates. We show our method outperforms natural alternatives.

Problem

• prediction-powered inference
• time series
• spatiotemporal data
• confidence intervals
• label imputation

Innovation

• Prediction-powered inference
• Spatiotemporal time series
• HAC procedures
• Confidence intervals
• Label imputation