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This paper introduces a novel prediction-powered inference (PPI) framework to address spatiotemporal time series forecasting with limited labeled data and abundant unlabeled covariates. The method extends existing PPI by incorporating Heteroskedasticity and Autocorrelation Consistent (HAC) procedures to handle temporal dependencies, thereby correcting for imputation bias in label estimation. The proposed approach yields reliable point estimates and confidence intervals, outperforming natural alternatives in scenarios with short labeled time series, long unlabeled time series, and an imperfect label predictor.
Spatiotemporal time series forecasting now boasts valid confidence intervals even with imputed labels and temporal dependencies, overcoming a critical limitation of existing PPI.
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.
