权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Estimation for non-linear processes with long memory

长记忆非线性过程的估计

基本信息

批准号：
1007616
负责人：
Murad Taqqu
金额：
$ 32.5万
依托单位：
Trustees of Boston University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2010
资助国家：
美国
起止时间：
2010-05-15 至 2014-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1007616&HistoricalAwards=false
关键词：
Estimation non linear processes long

项目摘要

Long-memory is characterized by a covariance function which decreases slowly to zero as the lag increases. The decrease is so slow that the corresponding spectral density blows up at very low frequencies, a phenomenon also known as ``long-range dependence'' or ``1/f noise''. Because wavelets are associated with scaling, it is natural to attempt to use wavelets in order to estimate the intensity of long memory in time series. The advantage of wavelets on Fourier methods is that there is no need to difference the time series if these are not stationary. Fourier and wavelet techniques have been applied to processes with long memory that are Gaussian or linear. This study focuses instead on non-linear processes with long memory, for example, outputs of non-linear filters with Gaussian or with linear inputs. The goal is to derive effective techniques to estimate the exponents which characterize the intensity of long-memory, in these more realistic contexts.Time series are a collection of data points collected through time, for instance income or temperature. The dependence between these data points may be weak or strong. When this dependence is strong the time series is said to have long memory. Time series with long memory appear in a number of applications, for example, in economics and in the analysis of traffic in computer networks. The goal of this study is to understand their properties and how to estimate them.

长记忆的特征在于协方差函数随着滞后的增加而缓慢地减小到零。这种下降是如此缓慢，以至于相应的谱密度在非常低的频率处爆炸，这种现象也被称为“长程相关”或“1/f噪声”。由于小波与尺度相关，因此很自然地尝试使用小波来估计时间序列中长记忆的强度。傅立叶方法小波的优点是，如果时间序列不是平稳的，就不需要对它们进行差分。傅立叶和小波技术已被应用于具有长记忆的高斯或线性过程。这项研究的重点，而不是与长记忆的非线性过程，例如，高斯或线性输入的非线性滤波器的输出。我们的目标是获得有效的技术来估计指数的特点的强度的长记忆，在这些更现实的context.Time序列是一个集合的数据点收集通过时间，例如收入或温度。这些数据点之间的相关性可能很弱或很强。当这种依赖性很强时，时间序列被称为具有长记忆。具有长记忆的时间序列出现在许多应用中，例如，在经济学和计算机网络中的流量分析中。本研究的目的是了解它们的性质以及如何估计它们。