Testing for a change of the long-memory parameter
Testing for a change of the long-memory parameter
复制标题
DOI：
10.1093/biomet/83.3.627
复制
发表时间：
1996-09
期刊：
影响因子：
2.7
通讯作者：
J. Beran;N. Terrin
中科院分区：
文献类型：
--
作者：
J. Beran;N. Terrin
长期相关性通常在长时间序列中观察到。当滞后k趋于无穷大时，相关性近似地像IkI 2”-2那样衰减，其中HE（0 5，1）。数据的长期特征基本上由参数H表征。H的微小变化对该过程的长期行为具有强烈的影响。特别地，均值和许多其他感兴趣的参数的估计量的收敛速度对于不同的H值是不同的。对于某些数据集，H似乎随时间而变化。在本文中，我们考虑一个简单的测试的零假设，H是常数。该测试是基于二次型的功能中心极限定理。给出了检验统计量的临界值。仿真验证了该方法的有效性。一个数据例子说明了它的实际应用。
SUMMARY Long-range dependence is often observed in long time series. Correlations decay approximately like Ik I2"-2, with H E (0 5, 1), as the lag k tends to infinity. The long-term features of the data are essentially characterised by the parameter H. Small changes of H have strong implications for the long-term behaviour of the process. In particular, rates of convergence of estimators for the mean, and for many other parameters of interest, differ for different values of H. For some data sets, H appears to change with time. In this paper we consider a simple test of the null hypothesis that H is constant. The test is based on a functional central limit theorem for quadratic forms. Critical values for the test statistic are given. Simulations confirm the validity of the test. A data example illustrates its practical application.