Prediction-powered inference for time series across space

@misc{rizvi2026predictionpowered,
  title = {{Prediction-powered inference for time series across space}},
  author = {Shahzar Rizvi and David Burt and Vishwak Srinivasan and Renato Berlinghieri and Stefano Del Col and Tamara Broderick},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08715},
  eprint = {2610.08715},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08715},
}

TY  - UNPB
TI  - Prediction-powered inference for time series across space
AU  - Shahzar Rizvi
AU  - David Burt
AU  - Vishwak Srinivasan
AU  - Renato Berlinghieri
AU  - Stefano Del Col
AU  - Tamara Broderick
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08715
UR  - https://arxiv.org/abs/2610.08715
AB  - 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.
ER  -