The study presents the results of research on two issues. The first issue is the modification to the Kettani and Gubner (2003) method of assessing the parameter of fractional integration in time series. In addition to the proposed modification, the study also presents the results of the research on the characteristics of fractional integration in the case of series with a small number of observations (100-1 000 observations). The results of the Monte Carlo simulation indicate that the applied modification contributes to a significant improvement in the accuracy of the approximations, especially in the case of series with a number of observations between 100 and 200, which is characteristic of the macroeconomic data.

The second issue is related to the verification, by means of the suggested method, of the hypothesis that long memory occurs in the GDP series of different countries. The hypothesis on the absence of the long memory was rejected in 12 cases out of 19 cases of series covering the period 1870-2001, while the remaining 7 cases produced inconclusive results. The results of the research coincide with those reported by Silverberg and Verspagen (1999) achieved with an alternative method of estimation. According to the author, the results of the research do not provide a clear answer to the question whether the GDP series have long memory, in other words, whether long non-periodical cycles occur in them.