An examination of performances of fractional unit-root tests using Monte-Carlo Simulationtechniques

In time series analysis, testing for stationarity is performed by unit root tests. However, in standard unit root tests, the degree of integration of the series typcially takes integer numbers. However, it has been revealed by studies that the power of the classical unit root tests is reduced when the series has a fractional integrated process. Therefore, tests have been developed to allow the degree of integration of the series to take fractional values. In this study, we investigate the performance of the fractional Dickey-Fuller tests and the augmented fractional Dickey-Fuller tests developed by Dolado, Gonzalo and Mayoral (2002) using Monte Carlo simulation methods. The simulation results show that size distortions occur when the fractional Dickey-Fuller and fractional augmented Dickey-Fuller tests include a deterministic component. In addition, in the case of augmented fractional Dickey-Fuller test, we improve possible size distortions using the sieve bootstrap method when the error term is autocorrelated. As an example to these methods, we test the validity of the weak form market efficiency for the 32 countries in the European region, which are classified according to their level of development. We find that the fraction of markets which are efficient in the weak form rises as the development levels of the countries increase.