Type I and type II fractional Brownian motions: A reconsideration
Type I and type II fractional Brownian motions: A reconsideration
复制标题
DOI：
10.1016/j.csda.2008.11.008
复制
发表时间：
2009-04
期刊：
影响因子：
--
通讯作者：
J. Davidson;N. Hashimzade
中科院分区：
文献类型：
--
作者：
J. Davidson;N. Hashimzade
所谓的I型和II型分数布朗运动是与分数积分模型相关联的极限分布，在分数积分模型中，前样本冲击被包括在滞后结构中，或者被抑制。这两个过程的分布和从它们导出的泛函的分布之间可能有很大的差异，因此决定使用哪种模型作为推理的基础成为一个重要的问题。替代方法模拟I型的情况下进行了对比，并接近非平稳边界的模型，截断无穷和的分布显着失真的结果。一个简单的模拟方法，克服了这个问题的描述和实施。该方法也有影响的估计I型ARFIMA模型，并提出了一个新的条件ML估计，使用每年的尼罗河最小值序列为例。
The so-called type I and type II fractional Brownian motions are limit distributions associated with the fractional integration model in which pre-sample shocks are either included in the lag structure, or suppressed. There can be substantial differences between the distributions of these two processes and of functionals derived from them, so that it becomes an important issue to decide which model to use as a basis for inference. Alternative methods for simulating the type I case are contrasted, and for models close to the nonstationarity boundary, truncating infinite sums is shown to result in a significant distortion of the distribution. A simple simulation method that overcomes this problem is described and implemented. The approach also has implications for the estimation of type I ARFIMA models, and a new conditional ML estimator is proposed, using the annual Nile minima series for illustration.