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A simple test for the equality of integration orders

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Abstract

A necessary condition for two time series to be nontrivially cointegrated is the equality of their respective integration orders. Thus, it is standard practice to test for order homogeneity prior to testing for cointegration. Tests for the equality of integration orders are particular cases of more general tests of linear restrictions among memory parameters of different time series, for which asymptotic theory has been developed in parametric and semiparametric settings. However, most tests have been developed in stationary and invertible settings, and, more importantly, many of them are invalid when the observables are cointegrated, because they usually involve inversion of an asymptotically singular matrix. We propose a general testing procedure which does not suffer from this serious drawback, and, in addition, it is very simple to compute, it covers the stationary/nonstationary and invertible/noninvertible ranges, and, as we show in a Monte Carlo experiment, it works well in finite samples.

Suggested Citation

  • Javier Hualde, 2012. "A simple test for the equality of integration orders," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 1206, Departamento de Economía - Universidad Pública de Navarra.
    • Handle: RePEc:nav:ecupna:1206
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    References listed on IDEAS

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    More about this item

    Keywords

    integration orders; fractional differencing; fractional cointegration.;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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