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Summability of stochastic processes: a generalization of integration and co-integration valid for non-linear processes

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  • Berenguer Rico, Vanessa

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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  • Berenguer Rico, Vanessa, 2011. "Summability of stochastic processes: a generalization of integration and co-integration valid for non-linear processes," UC3M Working papers. Economics we1115, Universidad Carlos III de Madrid. Departamento de Economía.
    • Handle: RePEc:cte:werepe:we1115
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    2. P.A.V.B. Swamy & I-Lok Chang & Jatinder S. Mehta & William H. Greene & Stephen G. Hall & George S. Tavlas, 2016. "Removing Specification Errors from the Usual Formulation of Binary Choice Models," Econometrics, MDPI, vol. 4(2), pages 1-21, June.
    3. Gadea Rivas, María Dolores & Gonzalo, Jesús, 2020. "Trends in distributional characteristics: Existence of global warming," Journal of Econometrics, Elsevier, vol. 214(1), pages 153-174.
    4. Markus Eberhardt, 2013. "Nonlinearities in the Relationship between Debt and Growth: Evidence from Co-Summability Testing," Discussion Papers 2013/06, University of Nottingham, Centre for Finance, Credit and Macroeconomics (CFCM).
    5. Hong, Seung Hyun & Wagner, Martin, 2011. "Cointegrating Polynomial Regressions," Economics Series 264, Institute for Advanced Studies.
    6. Chevillon, Guillaume & Mavroeidis, Sophocles, 2011. "Learning generates Long Memory," ESSEC Working Papers WP1113, ESSEC Research Center, ESSEC Business School.
    7. Markus Eberhardt & Andrea F. Presbitero, 2013. "This Time They’re Different: Heterogeneity and Nonlinearity in the Relationship between Debt and Growth," Discussion Papers 2013/10, University of Nottingham, Centre for Finance, Credit and Macroeconomics (CFCM).
    8. Banerjee Anurag & Pitarakis Jean-Yves, 2014. "Functional cointegration: definition and nonparametric estimation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(5), pages 507-520, December.

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    Keywords

    Co-integration;

    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; Diffusion Processes

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