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

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  • Berenguer-Rico, Vanessa
  • Gonzalo, Jesús

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.

Suggested Citation

  • Berenguer-Rico, Vanessa & Gonzalo, Jesús, 2014. "Summability of stochastic processes—A generalization of integration for non-linear processes," Journal of Econometrics, Elsevier, vol. 178(P2), pages 331-341.
    • Handle: RePEc:eee:econom:v:178:y:2014:i:p2:p:331-341
    DOI: 10.1016/j.jeconom.2013.08.031
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    2. Davide Delle Monache & Stefano Grassi & Paolo Santucci de Magistris, 2015. "Testing for Level Shifts in Fractionally Integrated Processes: a State Space Approach," CREATES Research Papers 2015-30, Department of Economics and Business Economics, Aarhus University.
    3. Ghoshray, A., 2018. "The Dynamic Properties of Natural Resource Prices," 2018 Conference, July 28-August 2, 2018, Vancouver, British Columbia 277210, International Association of Agricultural Economists.
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    6. Berenguer Rico, Vanessa, 2013. "Co-summability from linear to non-linear cointegration," UC3M Working papers. Economics we1312, Universidad Carlos III de Madrid. Departamento de Economía.
    7. Shinhye Chang & Matthew W. Clance & Giray Gozgor & Rangan Gupta, 2019. "A Reconsideration of Kuznets Curve across Countries: Evidence from the Co-summability Approach," Working Papers 201970, University of Pretoria, Department of Economics.
    8. Ben Nasr, Adnen & Gupta, Rangan & Sato, João Ricardo, 2015. "Is there an Environmental Kuznets Curve for South Africa? A co-summability approach using a century of data," Energy Economics, Elsevier, vol. 52(PA), pages 136-141.
    9. Kasparis, Ioannis & Andreou, Elena & Phillips, Peter C.B., 2015. "Nonparametric predictive regression," Journal of Econometrics, Elsevier, vol. 185(2), pages 468-494.
    10. Apergis, Nicholas & Christou, Christina & Gupta, Rangan, 2017. "Are there Environmental Kuznets Curves for US state-level CO2 emissions?," Renewable and Sustainable Energy Reviews, Elsevier, vol. 69(C), pages 551-558.
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    12. María Dolores Gadea Rivas & Jesús Gonzalo, 2022. "A tale of three cities: climate heterogeneity," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 13(1), pages 475-511, May.
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    14. Davide Delle Monache & Stefano Grassi & Paolo Santucci de Magistris, 2017. "Does the ARFIMA really shift?," CREATES Research Papers 2017-16, Department of Economics and Business Economics, Aarhus University.
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    18. Chevillon, Guillaume & Mavroeidis, Sophocles, 2018. "Perpetual learning and apparent long memory," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 343-365.

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    More about this item

    Keywords

    Co-integration; Co-summability; Integrated processes; Non-linear balanced relationships; Non-linear processes; Summability;
    All these keywords.

    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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