Modelling phase shifts among stochastic cycles

Abstract

Stochastic cycles are often incorporated in structural time series models to identify the cyclical components in macroeconomic time series. This paper proposes an extension of the multivariate stochastic cycle to account for phase shifts between individual cyclical components. The properties of the stochastic cycle allow phase shifts to be modelled in an entirely symmetrical way. As a result, cross correlations between cyclical components can be expressed in terms of phase shifts and phase‐adjusted associations. An application demonstrates the role of phase shifts in the business cycle relationships among output, total hours worked and the real wage in the United States.