An Extension of Cointegration to Fractional Autoregressive Processes

Soren Johansen

No 10-28, Discussion Papers from University of Copenhagen. Department of Economics

Abstract: This paper contains an overview of some recent results on the statistical analysis of cofractional processes, see Johansen and Nielsen (2010b). 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 β for which β′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 β 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.

Keywords: cofractional processes; cointegration rank; fractional cointegration; likelihood inference; vector autoregressive model (search for similar items in EconPapers)
JEL-codes: C32 (search for similar items in EconPapers)
Pages: 15 pages
Date: 2010-10
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Related works:
Working Paper: An extension of cointegration to fractional autoregressive processes (2011)
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Persistent link: https://EconPapers.repec.org/RePEc:kud:kuiedp:1028

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