Motivated by the application to German interest rates, we propose a time-varying autoregressive model for short-term and long-term prediction of time series that exhibit a temporary nonstationary behavior but are assumed to mean revert in the long run. We use a Bayesian formulation to incorporate prior assumptions on the mean reverting process in the model and thereby regularize predictions in the far future. We use MCMC-based inference by deriving relevant full conditional distributions and employ a Metropolis-Hastings within Gibbs sampler approach to sample from the posterior (predictive) distribution. In combining data-driven short-term predictions with long-term distribution assumptions our model is competitive to the existing methods in the short horizon while yielding reasonable predictions in the long run. We apply our model to interest rate data and contrast the forecasting performance to that of a 2-Additive-Factor Gaussian model as well as to the predictions of a dynamic Nelson-Siegel model.

中文翻译：

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用于改进短期和长期预测的贝叶斯时变自回归模型

受德国利率应用的启发，我们提出了一个时变自回归模型，用于短期和长期预测时间序列，该模型表现出暂时的非平稳行为，但从长远来看被假定为均值回复。我们使用贝叶斯公式在模型中加入对均值恢复过程的先验假设，从而规范远未来的预测。我们通过推导相关的完整条件分布来使用基于 MCMC 的推理，并在 Gibbs 采样器方法中使用 Metropolis-Hastings 从后验（预测）分布中进行采样。在将数据驱动的短期预测与长期分布假设相结合时，我们的模型在短期内与现有方法相比具有竞争力，同时在长期内产生合理的预测。