引入 CZAR 损失：针对金融对数收益预测的定制目标函数
Introducing the CZAR Loss: A Tailored Objective Function for Financial Log-Return Predictions
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中文总结 AI 辅助
针对金融对数收益预测中对称损失导致零预测偏差的问题，提出CZAR分段二次损失函数，在凸性、非对称惩罚等五要求下设计，实验证明其降低方向准确率阈值并提升大波动预测效果。
中文摘要 AI 辅助
在量化金融中，标准回归损失与收益预测的经济学原理不一致。由于金融对数收益的条件均值接近于零，均方误差和平均绝对误差等对称损失使得常数零预测成为近乎最优的解，从而惩罚了具有真实但含噪方向性技能的模型。这既适用于训练阶段（预测会向零收缩），也适用于评估阶段（平庸的预测器可能导致基于损失的排名失真）。在高斯线性预测模型下，我们证明所有对称单调损失相对于零预测器共享一个通用的盈亏平衡方向准确率，该准确率随着预测噪声接近收益的标准差而急剧上升并变得无法达到。我们引入了 CZAR（复合零无关收益）损失函数，这是一种分段二次损失，围绕五个关键要求构建：预测的凸性、随真实收益方向变化的非对称性（在零处消失）、对欠冲和错误方向预测的近似线性惩罚、对大误差的发散性，以及用于评估的自适应损失下限。CZAR 在固定真实值下可证明是预测的凸函数，具有适用于梯度提升库中自定义目标的闭式梯度和 Hessian 矩阵，其四个超参数通过相关默认值简化为单一选择。在理想化测试中，CZAR 评估的预测器在平均对数损失下超越零预测器所需的最小方向准确率保持在接近 50% 的机会水平，而对称损失的相应阈值随预测噪声急剧上升。这一优势在重尾收益分布下依然存在。在 BTC 日内对数收益的 LightGBM 实验中，CZAR 训练的模型减少了“零收益偏差”，并提高了大幅度收益的方向准确率。
英文摘要
In quantitative finance, standard regression losses are misaligned with the economics of return prediction. As the conditional mean of financial log-returns is close to zero, symmetric losses such as the mean squared and mean absolute errors make the constant zero forecast a near-optimal solution, penalizing models with genuine but noisy directional skill. This applies both during training, where predictions shrink toward zero, and during evaluation, where trivial forecasters can lead loss-based rankings. Under a Gaussian linear prediction model, we show that all symmetric monotonic losses share a universal breakeven directional accuracy against the zero predictor, which rises sharply and becomes unobtainable as the prediction noise approaches the standard deviation of the returns. We introduce the CZAR (Composite Zero-Agnostic Return) loss function, a piecewise quadratic loss built around five key requirements: convexity in the prediction, asymmetry with true return direction that vanishes at zero, near-linear penalization of undershoots and wrong-direction predictions, divergence for large errors, and an adaptive loss floor for evaluation. CZAR is provably convex in the prediction at fixed true value, has closed-form gradient and Hessian suitable for custom objectives in gradient-boosted libraries, and its four hyperparameters reduce to a single choice through correlated defaults. In idealized tests, the minimum directional accuracy required for a CZAR-evaluated forecaster to outperform the zero predictor under mean log loss remains near the 50% chance level, whereas the corresponding threshold for symmetric losses rises sharply with prediction noise. This advantage persists under heavy-tailed return distributions. In a LightGBM experiment on intraday BTC log-returns, CZAR-trained models reduce the `zero-returns bias' and improve directional accuracy on large-magnitude returns.
发表机构
- Allora Foundation（Allora基金会）
- Liverpool John Moores University（利物浦约翰摩尔大学）
机构由 AI 辅助整理，请以论文原文为准。
