In demographic literature, forecast uncertainty is often quantified with a statistical model. This model-based approach may potentially suffer from drawbacks, namely model misspecification, selection effect, and lack of finite-sample validity. We introduce a model-agnostic and distribution-free procedure, conformal prediction, for constructing prediction intervals for a functional time series. In the family of conformal prediction, split conformal prediction divides the data into training, validation, and test sets. Within the validation set, we can select optimal tuning parameters by calibrating the empirical coverage probabilities to match their nominal values. With the selected optimal tuning parameters, we then construct the prediction intervals using the same forecasting model for the holdout data in the testing set. Without sample splitting, sequential conformal prediction sequentially updates the predicted quantiles via an autoregressive process. Using Australian age- and sex-specific log mortality rates, we evaluate and compare the interval forecast accuracy, as measured by empirical coverage probability, coverage probability difference and mean interval score, between the two variants of conformal prediction.

翻译：在人口学文献中，预测不确定性通常通过统计模型进行量化。这种基于模型的方法可能面临模型设定错误、选择效应以及缺乏有限样本有效性等缺陷。本文引入一种与模型无关且无分布假设的方法——共形预测，用于构建函数型时间序列的预测区间。在共形预测家族中，分裂共形预测将数据划分为训练集、验证集和测试集。在验证集内，我们可以通过校准经验覆盖概率使其与名义值匹配，从而选择最优调优参数。基于选定的最优调优参数，我们利用相同的预测模型为测试集中的保留数据构建预测区间。在不进行样本分割的情况下，序列共形预测通过自回归过程逐步更新预测分位数。利用澳大利亚分年龄分性别的对数死亡率数据，我们评估并比较了两种共形预测变体的区间预测精度，具体指标包括经验覆盖概率、覆盖概率差异和平均区间得分。