EXACT LOCAL WHITTLE ESTIMATION OF FRACTIONAL INTEGRATION WITH UNKNOWN MEAN AND TIME TREND
EXACT LOCAL WHITTLE ESTIMATION OF FRACTIONAL INTEGRATION WITH UNKNOWN MEAN AND TIME TREND
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DOI：
10.1017/s0266466609100075
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发表时间：
2010-04-01
影响因子：
0.8
通讯作者：
Shimotsu, Katsumi
中科院分区：
文献类型：
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作者：
Shimotsu, Katsumi
最近，Shimotsu和Phillips （2005, Annals of Statistics 33, 1890-1933）提出了分数积分过程中记忆参数(d)的一种新的半参数估计，即精确局部Whittle （ELW）估计。如果优化覆盖宽度小于9/2的区间，且过程均值已知，则ELW估计量是一致的，对于所有的d值，它具有相同的N（0,1 /4）渐近分布。为了提供一个适合于经济数据的半参数估计量，我们扩展了ELW估计量，使其能够容纳未知均值和多项式时间趋势。我们证明了基于改进的ELW目标函数的两步ELW估计器，在第一阶段使用锥形局部Whittle估计器，对于d是（-1/ 2,2）的元素（或者当数据具有多项式趋势时d是（-1/ 2,7 /4）的元素）具有N（0,1 /4）渐近分布。仿真研究表明，两步ELW估计器继承了ELW估计器的优良特性。
Recently, Shimotsu and Phillips (2005, Annals of Statistics 33, 1890-1933) developed a new semiparametric estimator, the exact local Whittle (ELW) estimator, of the memory parameter (d) in fractionally integrated processes. The ELW estimator has been shown to be consistent, and it has the same N(0, 1/4) asymptotic distribution for all values of d, it the optimization covers an interval of width less than 9/2 and the mean of the process is known. With the intent to provide a semiparametric estimator Suitable for economic data, we extend the ELW estimator so that it accommodates an unknown mean and a polynomial time trend. We show that the two-step ELW estimator, which is based on a modified ELW objective function using a tapered local Whittle estimator in the first stage, has an N(0, 1/4) asymptotic distribution for d is an element of (-1/2, 2) (or d is an element of (-1/2, 7/4) when the data have a polynomial trend). Our Simulation study illustrates that the two-step ELW estimator inherits the desirable properties of the ELW estimator.