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Bayesian Analysis Of A Fractional Cointegration Model

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  • Gael Martin

Abstract

The concept of fractional cointegration, whereby deviations from an equilibrium relationship follow a fractionally integrated process, has attracted some attention of late. The extended concept allows cointegration to be associated with mean reversion in the error, rather than requiring the more stringent condition of stationarity. This paper presents a Bayesian method for conducting inference about fractional cointegration. The method is based on an approximation of the exact likelihood, with a Jeffreys prior being used to offset identification problems. Numerical results are produced via a combination of Markov chain Monte Carlo algorithms. The procedure is applied to several purchasing power parity relations, with substantial evidence found in favor of parity reversion.

Suggested Citation

  • Gael Martin, 2001. "Bayesian Analysis Of A Fractional Cointegration Model," Econometric Reviews, Taylor & Francis Journals, vol. 20(2), pages 217-234.
    • Handle: RePEc:taf:emetrv:v:20:y:2001:i:2:p:217-234
    DOI: 10.1081/ETC-100103824
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    2. repec:ebl:ecbull:v:3:y:2004:i:47:p:1-8 is not listed on IDEAS
    3. C.S. Forbes & G.M. Martin & J. Wright, 2002. "Bayesian Estimation of a Stochastic Volatility Model Using Option and Spot Prices," Monash Econometrics and Business Statistics Working Papers 2/02, Monash University, Department of Econometrics and Business Statistics.
    4. Gary Koop & Rodney Strachan & Herman van Dijk & Mattias Villani, 2004. "Bayesian Approaches to Cointegration," Discussion Papers in Economics 04/27, Division of Economics, School of Business, University of Leicester.
    5. Kleibergen, Frank, 2004. "Invariant Bayesian inference in regression models that is robust against the Jeffreys-Lindley's paradox," Journal of Econometrics, Elsevier, vol. 123(2), pages 227-258, December.
    6. Cunado, J. & Gil-Alana, L. A. & Perez de Gracia, F., 2004. "Is the US fiscal deficit sustainable?: A fractionally integrated approach," Journal of Economics and Business, Elsevier, vol. 56(6), pages 501-526.
    7. Luis A. Gil-Alana, 2004. "Fractional cointegration in the consumption and income relationship using semiparametric techniques," Economics Bulletin, AccessEcon, vol. 3(47), pages 1-8.

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    More about this item

    Keywords

    Fractional cointegration; Bayesian inference; Jeffreys prior; Markov chain Monte Carlo; JEL Classification: C11; C32;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • 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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