摘要翻译：
人们普遍认为，许多具有实际意义的时间序列具有很强的依赖性，即长记忆性。对于此类序列，样本自相关衰减较慢，对数周期图呈直线关系。这就需要有一类模型来描述这种行为。一个流行的此类模型是自回归分数积分移动平均(ARFIMA)，这是一个线性过程。然而，也需要非线性长记忆模型。例如，金融资产的收益率序列通常表现为零相关，而它们的平方或绝对值表现为长记忆性。此外，对产生长记忆的现实机制的探索导致了其他非线性长记忆模型的发展。在这一章中，我们将提出几个非线性长记忆模型，并讨论模型的性质，以及相关的参数估计和半参数估计。
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英文标题：
《Long Memory in Nonlinear Processes》
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作者：
Rohit Deo (IOMS), Meng-Chen Hsieh, Clifford M. Hurvich (IOMS),
  Philippe Soulier (MODAL'X)
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  It is generally accepted that many time series of practical interest exhibit strong dependence, i.e., long memory. For such series, the sample autocorrelations decay slowly and log-log periodogram plots indicate a straight-line relationship. This necessitates a class of models for describing such behavior. A popular class of such models is the autoregressive fractionally integrated moving average (ARFIMA) which is a linear process. However, there is also a need for nonlinear long memory models. For example, series of returns on financial assets typically tend to show zero correlation, whereas their squares or absolute values exhibit long memory. Furthermore, the search for a realistic mechanism for generating long memory has led to the development of other nonlinear long memory models. In this chapter, we will present several nonlinear long memory models, and discuss the properties of the models, as well as associated parametric andsemiparametric estimators.
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PDF链接：
https://arxiv.org/pdf/0706.1836