Spatial and spatio-temporal GARCH models

空间和时空 GARCH 模型

• 批准号: 412992257
• 负责人: Professor Dr. Philipp Otto
• 金额: --
• 依托单位: Zentrum für Informationsdienste und Hochleistungsrechnen (ZIH)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2018
• 资助国家: 德国
• 起止时间: 2017-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/412992257?language=en
• 关键词: Spatial; spatio; temporal; GARCH; models

The project aims to develop new models in spatial statistics, which deals with the analysis of random processes in space. Such processes are highly important in empirical research and particularly in econometrics. For instance, spatial statistics covers the analysis of processes on the surface of the Earth or the atmosphere, like air pollutants and particulate matters, regional prices for building land, or the population in municipalities. Generally, one can observe that observations, which are close together in space, are more similar than observations that are more distant in space; e.g., if the prices for building land are high in one municipality, then one might expect high prices in the neighboring municipalities. This phenomenon can be modeled by spatial autoregressive processes.Beside this spatial dependence of the observed values, an analog dependence can be observed for the variation of the data and the conditional heteroscedasticity. In this project, statistical models should be developed for data showing this behavior. In particular, the spatial model is defined in an analogous manner to the time-series ARCH model invented by Robert F. Engle (1982), who won the Nobel Memorial Prize in Economics for this theory in 2003.In addition, a multivariate spatial ARCH model should be introduced, such that several statistical variables can be modeled simultaneously, like for instance, several environmental pollutants and particulate matters. For this example, the spatial dependence is influenced by the wind direction and speed, which are in fact stochastic variables. Thus, a further aspect of the project is the analysis of stochastic spatial dependence and weighting schemes.

该项目旨在开发空间统计的新模型，该模型涉及空间随机过程的分析。这样的过程在实证研究中非常重要，尤其是在计量经济学中。例如，空间统计包括对地球表面或大气表面的过程进行分析，如空气污染物和颗粒物、建筑用地的区域价格或市政当局的人口。一般来说，人们可以观察到，在空间上靠近的观测比在空间上更远的观测更相似；例如，如果一个市政当局的建设用地价格很高，那么人们可能会认为邻近的市政当局的价格也会很高。这种现象可以用空间自回归过程来模拟，除了观测值的空间相关性外，数据的变化和条件异方差也可以观察到类似的相关性。在这个项目中，应该为显示这种行为的数据开发统计模型。特别是，空间模型的定义方式类似于2003年因该理论而获得诺贝尔经济学奖的罗伯特·F·恩格尔(Robert F.Engle)(1982)发明的时间序列ARCH模型。此外，还应引入多变量空间ARCH模型，以便可以同时对几个统计变量进行建模，例如几个环境污染物和颗粒物。在这个例子中，空间相关性受到风向和风速的影响，而风向和风速实际上是随机变量。因此，该项目的另一个方面是分析随机空间相关性和加权方案。