Small Sample Bootstrap Confidence Intervals for Long-Memory Parameter

The log periodogram regression is widely used in empirical applications because of its simplicity, since only a least squares regression is required to estimate the memory parameter, d, its good asymptotic properties and its robustness to misspecification of the short term behavior of the series. However, the asymptotic distribution is a poor approximation of the (unknown) finite sample distribution if the sample size is small. Here the finite sample performance of different nonparametric residual bootstrap procedures is analyzed when applied to construct confidence intervals. In particular, in addition to the basic residual bootstrap, the local and block bootstrap that might adequately replicate the structure that may arise in the errors of the regression are considered when the series shows weak dependence in addition to the long memory component. Bias correcting bootstrap to adjust the bias caused by that structure is also considered. Finally, the performance of the bootstrap in log periodogram regression based confidence intervals is assessed in different type of models and how its performance changes as sample size increases. Keywords—bootstrap, confidence interval, log periodogram regression, long memory. Authors are with Dpt. Econometrı́a y Estadı́stica, University of the Basque Country, Avda. Lehendakari Agirre 83, 48015 Bilbao, Spain (email: [email protected])