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

## TL;DR

This paper introduces an efficient approximation method for leave-future-out cross-validation in Bayesian time series models, enabling better future prediction assessment without extensive refitting.

## Contribution

It proposes a Pareto smoothed importance sampling approach to approximate exact LFO-CV, reducing computational costs and improving predictive accuracy evaluation.

## Key findings

- The method provides accurate approximations of LFO-CV.
- It significantly reduces computational time compared to exact methods.
- Diagnostics indicate the quality of the approximation is reliable.

## Abstract

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.