In this work, we present our findings of the so-called CIR#, which is a modified version of the Cox, Ingersoll, and Ross (CIR) model, turned into a forecasting tool for any term structure. The main feature of the CIR# model is its ability to cope with negative interest rates, cluster volatility, and jumps. By considering a dataset composed of money market interest rates during turmoil and calmer periods, we show how the CIR# performs in terms of directionality of rates and forecasting error. Comparison is carried out with a revamped version of the CIR model (denoted ), the Hull and White model, and the exponentially weighted moving average (EWMA) which is often adopted whenever no structure in data is assumed. To confirm the analysis, testing and validation is performed on both historical and ad hoc data with different metrics and clustering criteria.

中文翻译：

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利率预测：在 Hull 和 White 与 CIR#之间——如何使单因素模型发挥作用

在这项工作中，我们展示了我们对所谓的 CIR# 的发现，它是 Cox、Ingersoll 和 Ross (CIR) 模型的修改版本，变成了任何期限结构的预测工具。CIR# 模型的主要特征是它能够应对负利率、集群波动和跳跃。通过考虑由动荡时期和平静时期货币市场利率组成的数据集，我们展示了 CIR# 在利率方向性和预测误差方面的表现。使用 CIR 模型的改进版本进行比较（表示为)、赫尔和怀特模型，以及指数加权移动平均 (EWMA)，当没有假设数据中的结构时，通常采用指数加权移动平均 (EWMA)。为了确认分析、测试和验证，使用不同的指标和聚类标准对历史和临时数据执行。