In this paper we propose a new modelling framework for the analysis of macro series that includes both stochastic trends and stochastic cycles in addition to deterministic terms such as linear and non-linear trends. We examine four US macro series, namely annual and quarterly real GDP and GDP per capita. The results indicate that the behaviour of US GDP can be captured accurately by a model incorporating both stochastic trends and stochastic cycles that allows for somedegree of persistence in the data. Both appear to be mean-reverting, although the stochastic trend is nonstationary whilst the cyclical component is stationary, with cycles repeating themselves every 6-10 years.
GDP GDP per capita trends cycles long memory fractional integration