Modelling time series dynamics by cumulative error correction models

This study proposes a cumulated error correction model where the summing weights follow a geometrically decreasing function and are estimated from the data. It is shown that this approach nests the traditional error correction model – where no weight is given to deviations from steady state prior to the most recent period – and the cumulated error correction model, based on the idea of multicointegration. The latter assumes equal weights of one for past deviations.

The presented form of accumulation does not change the order of integration of the series, like in the multicointegration approach of Granger and Lee (1989). Therefore, typical cointegration test statistics remain valid. The resulting ECM possesses an ARMAX(1,0,1) representation. A cumulated ECM of this type uses in theory just one parameter more than the conventional one and is easy to apply in practice.

Based on this model type, two typical applications in economics are revisited: The US private consumption and the real money demand function. The short-run forces setting-off last period’s deviations are much smaller than a VEC or a conventional single equation ECM suggests. For the US it can be shown that GDP growth does not influence the short run real money demand apart from its cumulated deviation from steady state back into the far past.