Statistical analysis of high frequency intraday security prices

Existing return measure is not robust. We introduced the concept of "true daily price", and calculated return measure based on the estimator of the true price. The new return measure is robust and free of daily seasonality.; Currently, the connection of high frequency data with daily data is not well studied. We separated daily seasonality and daily volatility measures from high frequency data, and used the daily volatility series to improve interday volatility modeling. We constructed a discretized model to study daily volatility seasonality and derived the covariance matrix transaction by transaction. It shows that market open and market close the volatilities are higher than that at the middle of the day. We estimated the daily volatility characteristic and used the volatility series as the exogenous input to Enhanced Generalized Autoregressive Conditional Heteroscedastic (Enhanced GARCH) model, an extension of regular GARCH model. The new model generated higher likelihood than GARCH model.; We also studied the closing price return volatility by combining the result of intraday and interday volatility model. The volatility derived from the combined model has higher kurtosis than that from GARCH model, which matches empirical study better.