分整阶数半参数估计的有限样本性质研究

随着对经济和金融时间序列长记忆性的研究，分整阶数估计已成为当前理论研究的焦点问题。以对数周期图回归和局部Whittle方法为代表的半参数分整阶数估计方法在实践中得到广泛应用，但对这两类半参数估计方法的有限样本性质的比较则鲜有涉及，影响了在实践中对估计方法的选择。利用蒙特卡洛模拟方法，在不同数据产生的过程下，这两种半参数估计方法有限样本性质的研究结果表明：在ARFIMA(0, d, 0)过程下，LW类估计量具有较好的小样本性质；在平稳ARFIMA(1, d, 0)过程下，本文建议的QGPH估计量的有限样本性质要优于其他对数周期图估计量；在非平稳过程下，MGPH的偏差最小。

Finite Sample Properties of Semi-parametric Estimation of Fractional Integration

With the study of long memory in economic and financial time series, estimation of fractional integration order has become a focus in theory research. Semi-parametric estimation with log periodogram regression and local Whittle method as its representatives is widely used in practice, but comparison of finite sample properties of two classes of semi-parametric estimation methods is the least studied and it influences choice of estimation methods in practice. This article gives a comprehensive overview about these two classes of semi-parametric estimation methods in theory and uses Monte Carlo method to study finite sample properties of two classes of semi- parametric estimation under different data generation processes. The simulation reveals that: in ARFIMA(0, d, 0) process, the LW group estimators have better small sample properties; in ARFIMA(1, d, 0) process, the finite sample properties of QGPH estimator is better than other log periodogram estimators; in nonstationary process, the bias of MGPH estimators is minimum in all estimators.