A SEMIPARAMETRIC FREQUENCY DOMAIN APPROACH OF MODELLING THE REAL OUTPUT WITH FRACTIONAL INTEGRATION.

We propose in this article the use of the Quasi Maximum Likelihood Estimate of Robinson (QMLE, 1995a) for estimating the fractional differencing parameter in the real output and in the growth rate series of France, Italy and the U.K. This method is semiparametric and is robust to the different types of I(0) disturbances. The results indicate that the orders of integration of the real output are, in the three series, higher than 1 but smaller than 1.5, implying that their first differences are stationary but with long memory behaviour. However, the growth rates appear to be I(0) for the three countries. This may appear contradictory at first sight but it is explained by the non-linear log-transform involved. As a conclusion, the results show that the log-transformed series should be the data used in a multivariate framework when relating the real output with other variables in a cointegrating system.