Forecasting presents a complex estimation challenge, as it involves balancing multiple, often conflicting, priorities and objectives. Conventional forecast optimization methods typically emphasize a single metric--such as minimizing the mean squared error (MSE)--which may neglect other crucial aspects of predictive performance. To address this limitation, the recently developed Smooth Sign Accuracy (SSA) framework extends the traditional MSE approach by simultaneously accounting for sign accuracy, MSE, and the frequency of sign changes in the predictor. This addresses a fundamental trade-off--the so-called accuracy-smoothness (AS) dilemma--in prediction. We extend this approach to the multivariate M-SSA, leveraging the original criterion to incorporate cross-sectional information across multiple time series. As a result, the M-SSA criterion enables the integration of various design objectives related to AS forecasting performance, effectively generalizing conventional MSE-based metrics. To demonstrate its practical applicability and versatility, we explore the application of the M-SSA in three primary domains: forecasting, real-time signal extraction (nowcasting), and smoothing. These case studies illustrate the framework's capacity to adapt to different contexts while effectively managing inherent trade-offs in predictive modelling.

翻译：预测是一个复杂的估计问题，因为它需要平衡多个常常相互冲突的优先事项和目标。传统的预测优化方法通常强调单一指标——例如最小化均方误差（MSE）——这可能忽略了预测性能的其他关键方面。为应对这一局限，近期发展的平滑符号精度（SSA）框架扩展了传统的MSE方法，同时考虑了符号精度、MSE以及预测变量符号变化的频率。这解决了预测中的一个基本权衡——即所谓的精度-平滑度（AS）困境。我们将此方法扩展到多元M-SSA，利用原始准则来纳入多个时间序列的横截面信息。因此，M-SSA准则能够整合与AS预测性能相关的各种设计目标，有效地推广了传统的基于MSE的度量标准。为展示其实际适用性和多功能性，我们探讨了M-SSA在三个主要领域的应用：预测、实时信号提取（即时预测）和平滑。这些案例研究说明了该框架在不同情境下的适应能力，同时能有效管理预测建模中固有的权衡。