Title: Zero-crossings of time series: Sign-prediction, mean-square error and a holding-time constraint
Authors: Marc Wildi - Zurich University (Switzerland) [presenting]
Abstract: An extension of classic time series approaches is proposed which addresses zero-crossings of a zero-mean stationary time series. Specifically, we subject the original optimization criterion to a novel holding-time constraint which conditions the expected duration between consecutive crossings. Formally, the solution of this prediction problem is obtained by overlaying the classic estimate with a novel smoothing design whereupon the relative weight assigned to the latter by the criterion depends on the strength of the holding-time constraint. The resulting tradeoff is part of a general trilemma addressing smoothing, forecast accuracy and timeliness in prediction. Besides an analysis based on simple forecast and signal extraction exercises we also provide an application of our novel approach to business-cycle analysis. The examples illustrate that improved smoothing-capability (noise suppression) does not necessarily conflict with timeliness (relative lead) in this extended methodological framework.