Summability of stochastic processes: a generalization of integration and co-integration valid for non-linear processes
AbstractThe 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 (d): (i) generalizes I (d); (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 d 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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Bibliographic InfoPaper provided by Universidad Carlos III, Departamento de Economía in its series Economics Working Papers with number we1115.
Date of creation: Jun 2011
Date of revision:
Co-integration; Co-summability; Integrated processes; Non-linear balanced relationships; Non-linear processes; Summability;
Find related papers by JEL classification:
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-07-21 (All new papers)
- NEP-ECM-2011-07-21 (Econometrics)
- NEP-ORE-2011-07-21 (Operations Research)
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