The Accuracy Smoothness Dilemma in Prediction: a Novel Multivariate M-SSA Forecast Approach

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.