Geometric Structure Based High Frequency Data Distribution GARCH Model and Empirical Analysis

High frequency stock return data tend to exhibit characteristics such as volatility clustering, volatility persistence, leverage effects, and properties of abnormal unconditional distributions reflected in the form of skewness, high peakedness, and excess kurtosis. Although traditional GARCH models that employ leptokurtic distributions have been found useful to account for the conditional heteroscedasticity and leptokurtosis, most people directly apply the GARCH models to the raw data. This paper presents a novel geometric structure based on the raw data. We apply the GARCH models to the geometric structures. Preliminary tests generate a preponderance of evidence to support the innovative geometric structure specification over conventional competing alternatives presented in the literature.