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.

中文翻译：

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贝叶斯时间序列模型的近似离开未来交叉验证

时间序列分析的共同目标之一是使用观察到的序列为未来观察提供预测信息。在没有任何实际的新数据进行预测的情况下，交叉验证可用于估计模型未来的预测准确性，例如，用于模型比较或选择。贝叶斯模型的精确交叉验证通常计算量很大，但已经开发了近似交叉验证方法，最显着的是留一法交叉验证 (LOO-CV) 方法。如果实际的预测任务是根据过去预测未来，LOO-CV 提供了一个过于乐观的估计，因为来自未来观察的信息可用于影响过去的预测。为了正确解释时间序列结构，我们可以使用离开未来交叉验证 (LFO-CV)。与精确 LOO-CV 一样，精确 LFO-CV 需要针对不同的数据子集多次重新拟合模型。使用帕累托平滑重要性采样，我们提出了一种近似精确 LFO-CV 的方法，该方法大大降低了计算成本，同时还提供了关于近似质量的信息诊断。