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Summability of stochastic processes: a generalization of integration for non-linear processes
- Source :
- e-Archivo. Repositorio Institucional de la Universidad Carlos III de Madrid, instname
- Publication Year :
- 2014
- Publisher :
- Elsevier, 2014.
-
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 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. Financial support from SEJ-2007-63098, ECO-2010-19357, CONSOLIDER 2010 (CSD 2006-00016), and EXCELECON S-2007/HUM-044 grants is gratefully acknowledged.
- Subjects :
- Economics and Econometrics
Degree (graph theory)
Generalization
Stochastic process
Applied Mathematics
Mathematical analysis
Monte Carlo method
Integrated processes
Estimator
Co-integration
Variance (accounting)
Order of integration
Economía
Nonlinear system
Regressions
Applied mathematics
Co-summability
Non-linear processes
Summability
C22
Mathematics
Non-linear balanced relationships
C01
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- e-Archivo. Repositorio Institucional de la Universidad Carlos III de Madrid, instname
- Accession number :
- edsair.doi.dedup.....8abb46fcc41d63f1bc571d95830641f2