Approximate leave-future-out cross-validation for Bayesian time series models

Paul Christian Bürkner*, Jonah Gabry, Aki Vehtari

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

52 Citations (Scopus)
193 Downloads (Pure)


One of the common goals of time series analysis is to use the observed series to inform predictions for future observations. In the absence of any actual new data to predict, cross-validation can be used to estimate a model's future predictive accuracy, for instance, for the purpose of model comparison or selection. Exact cross-validation for Bayesian models is often computationally expensive, but approximate cross-validation methods have been developed, most notably methods for leave-one-out cross-validation (LOO-CV). If the actual prediction task is to predict the future given the past, LOO-CV provides an overly optimistic estimate because the information from future observations is available to influence predictions of the past. To properly account for the time series structure, we can use leave-future-out cross-validation (LFO-CV). Like exact LOO-CV, exact LFO-CV requires refitting the model many times to different subsets of the data. Using Pareto smoothed importance sampling, we propose a method for approximating exact LFO-CV that drastically reduces the computational costs while also providing informative diagnostics about the quality of the approximation.

Original languageEnglish
Pages (from-to)1-25
Number of pages25
Early online date1 Jan 2020
Publication statusPublished - 25 Jun 2020
MoE publication typeA1 Journal article-refereed


  • Bayesian inference
  • cross-Validation
  • pareto Smoothed importance sampling
  • Time series analysis


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