Publication: Summability of stochastic processes: a generalization of integration and co-integration valid for non-linear processes
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2011-06
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Berenguer Rico, Vanessa
Gonzalo, Jesús
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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.
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Keywords
Co-integration, Co-summability, Integrated processes, Non-linear balanced relationships, Non-linear processes, Summability