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

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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.