A Comparative Note about Estimation of the Fractional Parameter under Additive Outliers

In a recent paper, Fajardo et al. (2009) propose an alternative semiparametric estimator of the fractional parameter in ARFIMA models which is robust to the presence of additive outliers. The results are very interesting; however, they use samples of 300 or 800 observations which are rarely found in macroeconomics or economics. In order to perform a comparison, I use the procedure to detect for additive outliers based on the estimator Td suggested by Perron and Rodríguez (2003). Further, I use dummy variables associated to the location of the selected outliers to estimate the fractional parameter. I found better results for the mean and bias of this parameter when T = 100 and the results in terms of the standard deviation and the MSE are very similar. However, for higher sample sizes as 300 or 800, the robust procedure performs better, specially based on the standard deviation and MSE measures. Empirical applications for seven Latin American inflation series with very small sample sizes contaminated by additive outliers are discussed. What we find is that when no correction for additive outliers is performed, the fractional parameter is underestimated.

Keywords

Additive Outliers, ARFIMA Erros, Inflation, Semiparametric estimation

JEL Classification

C2, C3, C5