The order of integration is valid to characterize linear processes; but it is not appropriate for non-linearworlds. We propose the concept of summability (a re-scaled partial sum of the process being Op(1)) tohandle non-linearities. The paper shows that this new concept, S (δ): (i) generalizes I (δ); (ii) measuresthe degree of persistence as well as of the evolution of the variance; (iii) controls the balancedness ofnon-linear relationships; (iv) opens the door to the concept of co-summability which represents ageneralization of co-integration for non-linear processes. To make this concept empirically applicable,an estimator for δ and its asymptotic properties are provided. The finite sample performance ofsubsampling confidence intervals is analyzed via a Monte Carlo experiment. The paper finishes withthe estimation of the degree of summability of the macroeconomic variables in an extended version ofthe Nelson-Plosser database.
展开▼
