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.
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- Green open access
Cite this article
APA 7
Rizvi, S., Burt, D., Srinivasan, V., Berlinghieri, R., Del Col, S., & Broderick, T. (2026). Prediction-powered inference for time series across space. https://omanscience.com/en/articles/prediction-powered-inference-for-time-series-across-space
MLA 9
Rizvi, Shahzar, et al. "Prediction-powered inference for time series across space." https://omanscience.com/en/articles/prediction-powered-inference-for-time-series-across-space.
Chicago (author–date)
Rizvi, Shahzar, David Burt, Vishwak Srinivasan, Renato Berlinghieri, Stefano Del Col, and Tamara Broderick. 2026. "Prediction-powered inference for time series across space." https://omanscience.com/en/articles/prediction-powered-inference-for-time-series-across-space.
Harvard
Rizvi, S., Burt, D., Srinivasan, V., Berlinghieri, R., Del Col, S. and Broderick, T. (2026) 'Prediction-powered inference for time series across space', Available at: https://omanscience.com/en/articles/prediction-powered-inference-for-time-series-across-space.
Vancouver
Rizvi S, Burt D, Srinivasan V, Berlinghieri R, Del Col S, Broderick T. Prediction-powered inference for time series across space. https://omanscience.com/en/articles/prediction-powered-inference-for-time-series-across-space
IEEE
S. Rizvi, D. Burt, V. Srinivasan, R. Berlinghieri, S. Del Col, and T. Broderick, "Prediction-powered inference for time series across space," https://omanscience.com/en/articles/prediction-powered-inference-for-time-series-across-space.