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Nonstationary cointegration in the fractionally cointegrated VAR model

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  • Johansen, SÃÿren
  • ßrregaard Nielsen, Morten

Abstract

We consider the fractional cointegrated vector autoregressive (CVAR) model of Johansen and Nielsen (2012a) and make two distinct contributions. First, in their con- sistency proof, Johansen and Nielsen (2012a) imposed moment conditions on the errors that depend on the parameter space, such that when the parameter space is larger, stronger moment conditions are required. We show that these moment conditions can be relaxed, and for consistency we require just eight moments regardless of the pa- rameter space. Second, Johansen and Nielsen (2012a) assumed that the cointegrating vectors are stationary, and we extend the analysis to include the possibility that the cointegrating vectors are nonstationary. Both contributions require new analysis and results for the asymptotic properties of the likelihood function of the fractional CVAR model, which we provide. Finally, our analysis follows recent research and applies a parameter space large enough that the usual (non-fractional) CVAR model constitutes an interior point and hence can be tested against the fractional model using a x2-test.

Suggested Citation

  • Johansen, SÃÿren & ßrregaard Nielsen, Morten, 2018. "Nonstationary cointegration in the fractionally cointegrated VAR model," Queen's Economics Department Working Papers 274731, Queen's University - Department of Economics.
    • Handle: RePEc:ags:quedwp:274731
    DOI: 10.22004/ag.econ.274731
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    Keywords

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    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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