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Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model

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Author Info

  • Søren Johansen

    (Department of Economics, University of Copenhagen)

  • Morten Ørregaard Nielsen

    (Queen's University, Kingston, Ontario)

Abstract

We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model based on the conditional Gaussian likelihood. The model allows the process X(t) to be 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. The parameters d and b satisfy either d≥b≥1/2, d=b≥1/2, or d=d₀≥b≥1/2. Our main technical contribution is the proof of consistency of the maximum likelihood estimators on the set 1/2≤b≤d≤d₁ for any d₁≥d₀. To this end, we consider the conditional likelihood as a stochastic process in the parameters, and prove that it converges in distribution when errors are i.i.d. with suitable moment conditions and initial values are bounded. We then prove that the estimator of β is asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. We also find the asymptotic distribution of the likelihood ratio test for cointegration rank, which is a functional of fractional Brownian motion of type II.

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Bibliographic Info

Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 10-15.

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Length: 41 pages
Date of creation: May 2010
Date of revision:
Handle: RePEc:kud:kuiedp:1015

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Related research

Keywords: cofractional processes; cointegration rank; fractional cointegration; likelihood inference; vector autoregressive model;

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