Summability of stochastic processes—A generalization of integration for non-linear processes

Vanessa Berenguer-Rico and Jesus Gonzalo

Journal of Econometrics, 2014, vol. 178, issue P2, 331-341

Abstract: The 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 Op(1)) to handle non-linearities. The paper shows that this new concept, S(δ): (i) generalizes I(δ); (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 δ 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.

Keywords: Co-integration; Co-summability; Integrated processes; Non-linear balanced relationships; Non-linear processes; Summability (search for similar items in EconPapers)
JEL-codes: C01 C22 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (23)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:178:y:2014:i:p2:p:331-341

DOI: 10.1016/j.jeconom.2013.08.031

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