Spatial dual long memory processes – Definition, a semi-strong spatial FARIMAand a few spatial long memory volatility processes as individual or error models

空间双长记忆过程â定义，半强空间FARIMA和一些空间长记忆波动过程作为个体或误差模型

• 批准号: 530686798
• 负责人: Professor Dr. Yuanhua Feng
• 金额: --
• 依托单位: Lehrstuhl für Ökonometrie und quantitative Methoden der empirischen Wirtschaftsforschung
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/530686798?language=en
• 关键词: Spatial; dual; long; memory; processes

This project introduces the novel concept of “spatial dual long memory processes”. A general semi-strong spatial FARIMA (SFARIMA) framework with uncorrelated errors is first defined, which exhibits spatial dual long memory, i.e. simultaneous long memory in the first two conditional moments of a spatial process, if the errors have long memory in volatility. A spatial log-linear long memory volatility model, SFILog-GARCH, is first considered. Then time series and spatial double power extensions of the FIEGARCH (called PFIEGARCH and PSFIEGARCH) defined by the Box-Cox and signed power transformations of the magnitude and sign terms, respectively, will be introduced, where the two terms are with different power parameters. Another important contribution is the successful extension of the ARCH(∞) to an SARCH(∞), spatial ARCH(∞), including an SFIGARCH. The properties and estimation of those proposals will be investigated in detail. Non-stationary processes with memory parameter(s) bigger than 0.5 will also be studied. Spatial dual long memory, semiparametric and subordinated models will be further defined and discussed.

本项目引入了“空间对偶长记忆过程”的新概念。首先定义了具有不相关误差的一般半强空间FARIMA（SFARIMA）框架，如果误差在波动性中具有长记忆性，则该框架具有空间双重长记忆性，即空间过程的前两个条件时刻同时具有长记忆性。首先考虑了空间对数线性长记忆波动模型SFILog-GARCH。然后，时间序列和空间的双功率扩展的FIEG的（称为PFIEG和PSFIG的）定义的Box-Cox和符号功率变换的幅度和符号项，分别，将被引入，其中这两个术语是不同的功率参数。另一个重要的贡献是成功地将ε（∞）扩展到空间ε（∞），空间ε（∞），包括SFIG ε。这些建议的属性和估计将进行详细研究。还将研究记忆参数大于0.5的非平稳过程。空间双长记忆，半参数和从属模型将进一步定义和讨论。