A Note on the Size of the ADF Test with Additive Outliers and Fractional Errors. A Reapraisal about the (Non) Stationarity of the Latin-American Inflation Series.

This note analyzes the empirical size of the augmented Dickey and Fuller (ADF) statistic proposed by Perron and Rodríguez (2003) when the errors are frac- tional. This ADF is based on a searching procedure for additive outliers based on …rst-differences of the data named Tau- d. Simulations show that empirical size of the ADF is not affected by fractional errors con…rming the claim of Perron and Rodríguez (2003) that the procedure Tau-d is robust to departures of the unit root framework. In particular the results show low sensitivity of the size of the ADF statistic respect to the fractional parameter (d). However, as expected, when there is strong negative moving average autocorrelation or negative au- toregressive autocorrelation, the ADF statistic is oversized. These difficulties are …xed when sample increases (from T = 100 to T = 200). Empirical applica- tion to eight quarterly Latin-American ination series is also provided showing the importance of taking into account dummy variables for the detected additive outliers.