A simple test for the equality of integration orders
A necessary condition for two time series to be nontrivially cointegrated is the equality of their respective integration orders. Thus, it is standard practice to test for order homogeneity prior to testing for cointegration. Tests for the equality of integration orders are particular cases of more general tests of linear restrictions among memory parameters of different time series, for which asymptotic theory has been developed in parametric and semiparametric settings. However, most tests have been developed in stationary and invertible settings, and, more importantly, many of them are invalid when the observables are cointegrated, because they usually involve inversion of an asymptotically singular matrix. We propose a general testing procedure which does not suffer from this serious drawback, and, in addition, it is very simple to compute, it covers the stationary/nonstationary and invertible/noninvertible ranges, and, as we show in a Monte Carlo experiment, it works well in finite samples.
|Date of creation:||2012|
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- Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, vol. 105(1), pages 225-247, November.
- P. M. Robinson & J. Hualde, 2003.
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- D Marinucci & Peter M. Robinson, 2001. "Semiparametric fractional cointegration analysis," LSE Research Online Documents on Economics 2269, London School of Economics and Political Science, LSE Library.
- Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
- D Marinucci & Peter M Robinson, 2001. "Semiparametric Fractional Cointegration Analysis," STICERD - Econometrics Paper Series 420, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
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