Cointegration of nonstationary time series is considered in a fractional context. Both the observable series and the cointegrating error can be fractional processes. The familiar situation in which the respective integration orders are 1 and 0 is nested, but these values have typically been assumed known. We allow one or more of them to be unknown real values, in which case Robinson and Marinucci (1997,2001) have justified least squares estimates of the cointegrating vector, as well as narrow-band frequencydomain estimates, which may be less biased. While consistent, these estimates do not always have optimal convergence rates, and they have non-standard limit distributional behaviour. We consider estimates formulated in the frequency domain, that consequently allow for a wide variety of (parametric) autocorrelation in the short memory input series, as well as time-domain estimates based on autoregressive transformation. Both can be interpreted as approximating generalized least squares and Gaussian maximum likelihood estimates. The estimates share the same limiting distribution, having mixed normal asymptotics (yielding Wald test statistics with null limit distributions), irrespective of whether the integration orders are known or unknown, subject in the latter case to their estimation with adequate rates of convergence. The parameters describing the short memory stationary input series are -consistently estimable, but the assumptions imposed on these series are much more general than ones of autoregressive moving average type. A Monte Carlo study of finite-sample performance and an empirical application to testing the PPP hypothesis are included.
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Paper provided by School of Economics and Business Administration, University of Navarra in its series Faculty Working Papers with number
07/02.
Length: 48 pages pages Date of creation: Nov 2002 Date of revision: Publication status: Published, Econometrica, 2003, vol. 71(6): pp. 1727-1766 Handle: RePEc:una:unccee:wp0702
Find related papers by JEL classification: C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
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Carlos Pestana Barros & João Ricardo Faria & Luis A. Gil-Alana, 2008.
"Persistence in Airline Accidents,"
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2008/18, Department of Economics at the School of Economics and Management (ISEG), Technical University of Lisbon..
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