Department of Economics and Business Economics

An extension of cointegration to fractional autoregressive processes

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    Submitted manuscript, 596 KB, PDF document

  • School of Economics and Management
  • Centre for Research in Econometric Analysis of Time Series (CREATES)
This paper contains an overview of some recent results on the statistical analysis of cofractional processes, see Johansen and Nielsen (2010). We first give an brief summary of the analysis of cointegration in the vector autoregressive model and then show how this can be extended to fractional processes. The model allows the process X(t) to be fractional of order d and cofractional of order d-b>0; that is, there exist vectors beta for which beta'X(t) is fractional of order d-b. We analyse the Gaussian likelihood function to derive estimators and test statistics. The asymptotic properties are derived without the Gaussian assumption, under suitable moment conditions. We assume that the initial values are bounded and show that they do not influence the asymptotic analysis The estimator of \beta is asymptotically mixed Gaussian and estimators of the remaining parameters are asymptotically Gaussian. The asymptotic distribution of the likelihood ratio test for cointegration rank is a functional of fractional Brownian motion.
Original languageEnglish
Place of publicationAarhus
PublisherCREATES, Institut for Økonomi, Aarhus Universitet
Number of pages15
Publication statusPublished - 1 Feb 2011

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