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

Abstract

This note analyzes the empirical size of the augmented Dickey and Fuller (ADF) statistic proposedby Perron and Rodríguez (2003) when the errors are fractional. This ADF is based on a searching procedure for additive outliers based on first-differences of the data named td. Simulations show that empirical size of the ADF is not affected by fractional errors confirming the claim of Perron and Rodríguez (2003) that the procedure td 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 autoregressive autocorrelation, the ADF statistic is oversized. These difficulties are fixed when sample increases (from T = 100 to T = 200). Empirical application to eight quarterly Latin American inflation series is also provided showing the importance of taking into account dummy variables for the detected additive outliers.