Testing of fractional cointegration in macroeconomic time series

We propose in this article a two-step testing procedure of fractional cointegration in macroeconomic time series. It is based on Robinson’s (1994) univariate tests and is similar in spirit to the one proposed by Engle and Granger (1987), testing initially the order of integration of the individual series and then, testing the degree of integration of the residuals from the cointegrating relationship. Finite-sample critical values of the new tests are computed and Monte Carlo experiments are conducted to examine the size and the power properties of the tests in finite samples. An empirical application, using the same datasets as in Engle and Granger (1987) and Campbell and Shiller (1987) is also carried out at the end of the article. -- Fractional cointegration ; Long memory