The analysis of complex survey responses, including correlated time-series, has for long received thorough treatment. However, the difficulty with the current literature on inference for correlated time-series survey responses is its rigidness in target population quantities. Incidentally, practitioners are finding uses of sampling methodology because of technological limitations, also needing more complex analyses. Estimators and confidence intervals can, and have been, derived for population totals and averages, but not for generic summaries like subgroup averages or group differences.
We enhance the current methodology for correlated time-series survey responses in the model-assisted framework. We make use of Gaussian Process regression models to improve inference and we show the ease with which these results can be extended to generic summaries. These models also allow for domain-specific knowledge to be encoded into the prior to further improve estimation. Through simulation, this strategy is shown to outperform other model-assisted estimators in terms of estimation performance and inference. We also showcase the procedure in electricity usage data.