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Econometrics: Non-linear Cointegration

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Encyclopedia of Complexity and Systems Science

Definition of the Subject

This paper is a selective review of the literature on nonlinear cointegration and nonlinear error correction models. The concept ofcointegration plays a major role in macroeconomics, finance and econometrics. It was introduced by Granger in [42] and since then, it has achieved immense popularity among econometricians and applied economists. In fact in 2003the Royal Swedish Academy of Science gave the Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel to C. W. J. Granger for his contributionto the analysis of economic relationships based on cointegrated variables. In this paper we discuss the nonlinear extensions of the linear cointegrationtheory. Some authors consider nonlinear cointegration as a particular case of nonlinear error correction models. Although both concepts are related,we believe that it is useful to distinguish between them. After making this point clear, by relating linear and nonlinear error correction models, wediscuss...

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Abbreviations

Cointegration :

Cointegration is an econometric property relating time series variables. If two or more series are themselves nonstationary, but a linear combination of them is stationary, then the series are said to be cointegrated.

Short memory :

A time series is said to be short memory if its information decays through time. In particular, we say that a variable is short memory in mean (in distribution), if the conditional mean (distribution) of the variable at time t given the information at time \( { t-h } \) converges to a constant (to an unconditional distribution) as h diverges to infinity. Shocks in short memory time series have transitory effects.

Extended memory :

A time series is said to be extended memory in mean (in distribution), if it is not short memory in mean (distribution). Shocks in extended memory time series have permanent effects.

Nonlinear cointegration :

If two or more series are of extended memory, but a nonlinear transformation of them is short memory, then the series are said to be nonlinearly cointegrated.

Error correction model :

An Error Correction Model is a dynamic model in which the rate of growth of the variables in any period is related to the previous period's gap from long-run equilibrium.

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Author information

Authors and Affiliations

  1. Department of Economics, Indiana University, Bloomington, USA

    Juan-Carlos Escanciano

  2. Department of Economics, Universidad Carlos III de Madrid, Madrid, Spain

    Alvaro Escribano

Authors
  1. Juan-Carlos Escanciano
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Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Escanciano, JC., Escribano, A. (2009). Econometrics: Non-linear Cointegration. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_166

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