Garry D. A. Phillips

In this paper we extend the results in [5] in two directions: First, we show that by bias correcting the estimated mean reversion parameter we can also have better finite sample properties of the testing procedure using a t-statistic in the near unit root situation when the mean reversion parameter is approaching its lower bound versus using the Jackknife estimator of Phillips and Yu [8]. Second, we show that although Tang and Chen [10] demonstrate that the variance of the maximum likelihood estimator of the long term mean parameter is of an order equal to the reciprocal of the sample size (the same order as that of the bias and variance of the mean reversion parameter estimator and so it does not converge very fast to its true value), the t-statistic related to that parameter does not exhibit large empirical size distortions and so does not need to be bias corrected in practice.

This article considers the modelling of short-term interest rates with the ARFIMA model in six European countries based on daily data in the 1990s using the Modified Profile Likelihood estimation method. This allows one to study the different convergence processes that have been followed in each case. Empirical evidence shows that, even with this estimation method, the standard AIC tends to select models that in some cases are in accordance with traditional inference but in other cases may not be so. Analysing these results, the series for Switzerland appears to be an I(1) series, which conflicts with the findings in previous literature.