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Likelihood inference for a fractionally cointegrated vector autoregressive model

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  • Søren Johansen

    () (University of Copenhagen and CREATES)

  • Morten Ørregaard Nielsen

    () (Queen`s University and CREATES)

Abstract

We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model, based on the Gaussian likelihood conditional on initial values. We give conditions on the parameters such that the process X_{t} is fractional of order d and cofractional of order d-b; that is, there exist vectors β for which β′X_{t} is fractional of order d-b, and no other fractionality order is possible. For b=1, the model nests the I(d-1) VAR model. We define the statistical model by 0 1/2, we prove that the limit distribution of T^{b₀}(β-β₀) is mixed Gaussian and for the remaining parameters it is Gaussian. The limit distribution of the likelihood ratio test for cointegration rank is a functional of fractional Brownian motion of type II. If b₀

Suggested Citation

  • Søren Johansen & Morten Ørregaard Nielsen, 2010. "Likelihood inference for a fractionally cointegrated vector autoregressive model," Working Papers 1237, Queen's University, Department of Economics.
  • Handle: RePEc:qed:wpaper:1237
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    File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1237.pdf
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    More about this item

    Keywords

    Cofractional processes; cointegration rank; fractional cointegration; likelihood inferencw; vector autoregressive model;

    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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