Additive fractional models for large random fields applied to high-frequency financial data

我们建议将非负高频金融数据（如平方收益和波动率指数）表示为晶格上的随机场，其中晶格由交易日和一天的交易时间点定义。这些数据可以通过Box-Cox变换使用加性空间模型进行分析。本项目的目标是同时在两个维度上估计一个非平稳光滑回归曲面和一个具有短记忆和长记忆以及反持久性的平稳分量。采用快速双条件平滑技术拟合回归曲面。将使用迭代插件算法选择带宽。然后使用空间FARIMA模型估计平稳分量。Box-Cox-Transformation对结果估计量的影响将被详细研究。还将讨论可能的扩展和一些进一步的问题。这些建议的实际意义将通过应用和仿真来说明。该项目的结果也可以很容易地进行调整，以分析其他研究领域的类似空间数据，如物理、医学、生物学和生态学。

We propose to represent nonnegative high-frequency financial data such as squared returns and volatility indexes as random fields on a lattice, where the lattice is defined by the trading days and the trading time points on a day. These data can be analyzed using an additive spatial model by means of the Box-Cox transformation. The goal of this project is to estimate a nonstationary smooth regression surface and a stationary component with short- and long memory as well as antipersistence in both dimensions simultaneously. The regression surface is fitted using a quick double conditional smoothing technique. The bandwidths will be selected with an iterative plug-in algorithm. The stationary components are then estimated using a spatial FARIMA model. The effects of the Box-Cox-Transformation on the resulting estimators will be investigated in detail. Possible extensions and some further problems will also be discussed. The practical relevance of the proposals will be illustrated through application and simulation. The results of this project can also be easily adjusted to analyze similar spatial data from other research areas, such as Physics, Medicine, Biology and Ecology.