Beyond Co-Integration: Modelling Co-Movements in Macro finance

Macroeconomic and aggregate financial series share an unconventional type of nonlinear dynamics. Existing techniques (like co-integration) model these dynamics incompletely, hence generating seemingly paradoxical results. To avoid this, we provide a methodology to disentangle the long-run relation between variables from their own dynamics, and illustrate with two applications. First, in the forward-premium puzzle, adding a component quantifying the persistent nonlinear dynamics of exchange rates yields substantial predictability and makes the forward-premium term insignificant. Second, S&P 500 grows in a pattern of momentum followed by reversal, forming long cycles around a trend given by GDP, a stable non-breaking relation since WWII.