基于预筛选筛自助法的函数型时间序列长记忆估计量的偏差校正
Bias Correction of Long-memory Estimator of Functional Time Series via the Prefiltered Sieve Bootstrap
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中文总结 AI 辅助
该研究针对函数型时间序列长记忆参数估计的偏差问题，提出基于预筛选筛自助法的校正程序，采用LPWN估计量作为初始估计，经模拟验证其能有效降低偏差并可提供参数置信区间。
中文摘要 AI 辅助
我们研究一种基于筛自助法的偏差校正程序，用于估计平稳或非平稳分数整合过程中的长记忆参数d。该重采样方法对经长记忆参数初步估计量预筛选后的数据实施筛自助法，对于初始估计量，我们推荐采用Frederiksen等人（2012）提出的带噪声的局部多项式Whittle（LPWN）估计量，以减少偏差，尤其在存在强短期自回归依赖的情况下。通过一系列模拟研究，我们首先指出使用局部Whittle或去趋势波动分析估计量时存在的偏差问题，随后考虑LPWN估计量，证明其经筛自助法增强后在偏差校正方面的潜在改进。作为副产品，该筛自助法还可提供记忆参数的置信区间。
英文摘要
We investigate a bias correction procedure based on sieve bootstrapping to estimate the long-memory parameter d in stationary or nonstationary fractionally integrated processes. The resampling method implements a sieve bootstrap method on data prefiltered by a preliminary estimate of the long-memory parameter. For the initial estimate, we recommend the local polynomial Whittle with noise (LPWN) estimator in Frederiksen et al. (2012) to reduce bias, especially in the presence of a strong short-range autoregressive dependence. Through a series of simulation studies, we first highlight the issue of bias, using the local Whittle or detrended fluctuation analysis estimator. Then, we consider the LPWN estimator and show the potential improvement in bias achieved by its sieve bootstrap enhancement. As a byproduct, the sieve bootstrap can also provide confidence intervals of the memory parameter.
