Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model
AbstractWe 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 Î² for which Î²â²X(t) is fractional of order d-b. The parameters d and b satisfy either dâ¥bâ¥1/2, d=bâ¥1/2, or d=dââ¥bâ¥1/2. Our main technical contribution is the proof of consistency of the maximum likelihood estimators on the set 1/2â¤bâ¤dâ¤dâ for any dââ¥dâ. 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 Î² 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 InfoArticle provided by Econometric Society in its journal Econometrica.
Volume (Year): 80 (2012)
Issue (Month): 6 (November)
Other versions of this item:
- Søren Johansen & Morten Ørregaard Nielsen, 2010. "Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model," Discussion Papers 10-15, University of Copenhagen. Department of Economics.
- Søren Johansen & Morten Ørregaard Nielsen, 2010. "Likelihood inference for a fractionally cointegrated vector autoregressive model," CREATES Research Papers 2010-24, School of Economics and Management, University of Aarhus.
- Søren Johansen & Morten Ørregaard Nielsen, 2010. "Likelihood inference for a fractionally cointegrated vector autoregressive model," Working Papers 1237, Queen's University, Department of Economics.
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
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