Diagnostic Testing For Cointegration
AbstractWe develop a sequence of tests for specifying the cointegrating rank of, possiblyfractional, multiple time series. Memory parameters of observables are treated asunknown, as are those of possible cointegrating errors. The individual test statisticshave standard null asymptotics, and are related to Hausman specification teststatistics: when the memory parameter is common to several series, an estimate ofthis parameter based on the assumption of no cointegration achieves an efficiencyimprovement over estimates based on individual series, whereas if the series arecointegrated the former estimate is generally inconsistent. However, acomputationally simpler but asymptotically equivalent approach, which avoidsexplicit computation of the "efficient" estimate, is instead pursued here. Twoversions of it are initially proposed, followed by one that robustifies to possibleinequality between memory parameters of observables. Throughout, asemiparametric approach is pursued, modelling serial dependence only atfrequencies near the origin, with the goal of validity under broad circumstances andcomputational convenience. The main development is in terms of stationary series,but an extension to nonstationary ones is also described. The algorithm forestimating cointegrating rank entails carrying out such tests based on potentially allsubsets of two or more of the series, though outcomes of previous tests mayrender some or all subsequent ones unnecessary. A Monte Carlo study of finitesample performance is included.
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Bibliographic InfoPaper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2007/522.
Date of creation: Sep 2007
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Fractional cointegration; Diagnostic testing; Specificationtesting; Cointegrating rank; Semiparametric estimation.;
Find related papers by JEL classification:
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-02-02 (All new papers)
- NEP-ECM-2008-02-02 (Econometrics)
- NEP-ETS-2008-02-02 (Econometric Time Series)
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