Sign Accuracy, Mean-Squared Error and the Rate of Zero Crossings: a Generalized Forecast Approach

TL;DR

This paper introduces the SSA framework, a new forecasting approach that balances sign accuracy, MSE, and sign change frequency, addressing the trade-offs in predictive performance and extending to non-stationary processes.

Contribution

The paper presents the SSA criterion, a novel method that generalizes traditional MSE-based metrics by incorporating sign accuracy and smoothness considerations in forecasting.

Findings

SSA effectively balances accuracy and smoothness in forecasts.

The methodology extends to non-stationary, integrated processes.

Application to business cycle analysis demonstrates versatility.

Abstract

Forecasting entails a complex estimation challenge, as it requires balancing multiple, often conflicting, priorities and objectives. Traditional forecast optimization criteria typically focus on a single metric -- such as minimizing the mean squared error (MSE) -- which may overlook other important aspects of predictive performance. In response, we introduce a novel approach called the Smooth Sign Accuracy (SSA) framework, which simultaneously considers 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. The SSA criterion thus enables the integration of various design objectives related to AS forecasting performance, effectively generalizing conventional MSE-based metrics. We further extend this methodology to accommodate non-stationary, integrated processes, with particular emphasis on controlling the predictor's monotonicity. Moreover, we demonstrate the broad applicability of our approach through an application to, and customization of, established business cycle analysis tools, highlighting its versatility across diverse forecasting contexts.