Between cointegration and multicointegration: Modelling time series dynamics by cumulative error correction models

This study proposes a cumulative error correction model where the summing weights follow a geometrically decreasing function of prior deviations from the equilibrium and are estimated from the data. It is shown that this approach nests both the traditional error correction model – where no weight is given to deviations from the steady state prior to the most recent period – and the error correction model based on the idea of multicointegration. The form of accumulation presented here does not change the order of integration of the series, as is the case in the multicointegration approach of Granger and Lee (1989). Furthermore, it is very parsimonious as only one or two parameters more have to be estimated. The assumption of geometrically decreasing weights can be tested by estimating the model in its unrestricted form. Based on this new model type, the relationship between private consumption and real disposable income of private households in the US is estimated. The short-term forces which set off the most recent period's deviations are much smaller than would be suggested by a VEC and a conventional single equation ECM, and the income elasticity is lower as well. The proposed model outperforms the other two with respect to its forecasting power. ► A modification of the error correction model (ECM) is proposed. ► Not only the deviation from steady-state of the most recent period is considered. ► Deviations of the past are cumulated by geometrically decreasing weights. ► The model nests the traditional ECM as well as the multi-cointegration approach. ► As an empirical application the short-run dynamics of US consumption are modelled.