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Local Whittle Analysis of Stationary Unbalanced Fractional Cointegration Systems

Author

Listed:
  • Gilles de Truchis

    (EconomiX - EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

  • Florent Dubois

    (EconomiX - EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

  • Elena Ivona Dumitrescu

    (EconomiX - EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper we propose a local Whittle estimator of stationary bivariate unbalanced fractional cointegration systems. Unbalanced cointegration refers to the situation where the observables have different integration orders, but their filtered versions have equal integration orders and are cointegrated in the usual sense. Based on the frequency domain representation of the unbalanced version of Phillips' triangular system, we develop a semiparametric approach to jointly estimate the unbalance parameter, the long run coefficient, and the integration orders of the regressand and cointegrating errors. The paper establishes the consistency and asymptotic normality of this estimator. We find a peculiar rate of convergence for the unbalance estimator (possibly faster than root-n) and a singular joint limiting distribution of the unbalance and long-run coefficients. Its good finite-sample properties are emphasized through Monte Carlo experiments. We illustrate the relevance of the developed estimator for financial data in an empirical application to the information flowing between the crude oil spot and CME-NYMEX markets.

Suggested Citation

  • Gilles de Truchis & Florent Dubois & Elena Ivona Dumitrescu, 2019. "Local Whittle Analysis of Stationary Unbalanced Fractional Cointegration Systems," Working Papers hal-04141882, HAL.
    • Handle: RePEc:hal:wpaper:hal-04141882
    Note: View the original document on HAL open archive server: https://hal.science/hal-04141882
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    References listed on IDEAS

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