Berenguer Rico, VanessaGonzalo Muñoz, Jesús2022-09-142022-09-142014-01-01Berenguer-Rico, V., & Gonzalo, J. (2014). Summability of stochastic processes-A generalization of integration for non-linear processes. Journal of Econometrics, 178, pp. 331-341.0304-4076https://hdl.handle.net/10016/35700The order of integration is valid to characterize linear processes; but it is not appropriate for non-linear worlds. We propose the concept of summability (a re-scaled partial sum of the process being O-p(1)) to handle non-linearities. The paper shows that this new concept, S (delta): (i) generalizes I (delta); (ii) measures the degree of persistence as well as of the evolution of the variance; (iii) controls the balancedness of non-linear relationships; (iv) opens the door to the concept of co-summability which represents a generalization of co-integration for non-linear processes. To make this concept empirically applicable, an estimator for delta and its asymptotic properties are provided. The finite sample performance of subsampling confidence intervals is analyzed via a Monte Carlo experiment. The paper finishes with the estimation of the degree of summability of the macroeconomic variables in an extended version of the Nelson-Plosser database.eng© 2013 Elsevier B.V. All rights reservedAtribución-NoComercial-SinDerivadas 3.0 EspañaCo-integrationCo-summabilityIntegrated processesNon-linear balanced relationshipsNon-linear processesSummabilityRegressionsresearch articleC01C22Economíahttps://doi.org/10.1016/j.jeconom.2013.08.031open access331Part 2341JOURNAL OF ECONOMETRICS178AR/0000014556