Fractional Integration in Short Samples: Parametric Versus Semiparametric Methods

Abstract

The finite sample properties of various parametric and semiparametric estimators of fractional integration are determined using Monte Carlo simulations. Previous work investigating the performance of fractional estimators relied on large sample sizes typical of economic and finance data sets. Here, the simulations are run with sample sizes representative of data sets commonly found in political science - between 40 and 100. Simulations are run on three different data generating processes (0, d, 0), (1, d, 0), and (0,d,1), with the AR and MA parameters and the order of fractional integration, d, varying with the order of fractional integration. The results indicate that semiparametric methods and the parametric frequency domain Whittle estimator are consistent across all ranges of observations with a purely fractional, (0,d,0) process, while the parametric time domain estimator exhibits a negative bias in its estimates. In the presence of a higher-order process the time domain estimator suffers dramatically and the semiparamteric estimators also exhibit bias that is potentially alleviated with proper choice of bandwidth. Throughout, the frequency domain maximum likelihood estimator outperforms other estimators, even in the presence of significant higher frequencies. The results indicate that fractional integration can be reliably estimated with lag lengths of 80 observations, but caution is still urged, particularly with the time domain estimator.