Business-Cycle Analysis and Zero-Crossings of Time Series: A Generalized Forecast Approach

We propose an extension of classic time series approaches to business-cycle measurement called Simple Sign Accuracy (SSA), which addresses zero-crossings of a zero-mean stationary time series. Zero-crossings or sign-changes of the growth-rate of an economic indicator mark transitions between expansion and contraction episodes which can be related to business-cycles. The length or, more specifically, the mean duration between consecutive zero-crossings of a predictor, can be controlled in our approach by subjecting a variation of the classic optimization criterion to a novel ‘holding time’ constraint. The proposed criterion embodies a prediction trilemma which recognizes the fundamental trade-offs between accuracy, timeliness and smoothness (ATS). As a result, the SSA-criterion can address a multiplicity of design priorities in terms of ATS forecast performances, and the classic mean-square error paradigm is obtained as a special case when assigning weight only to the accuracy component. We also show that SSA can be interpreted as an extension of classic smoothing algorithms and that the approach lends itself for customization of existing benchmark predictors. The latter possibility is exploited in a real-time analysis (nowcasting) of the US business cycle, whereby SSA is plugged onto a well-known benchmark to modify the latter’s characteristics in terms of ATS performances.