Statistical properties, dynamic conditional correlation and scaling analysis: Evidence from Dow Jones and Nasdaq high-frequency data

This paper investigates statistical properties of high-frequency intraday stock returns across various frequencies. Both time series and panel data are utilized to explore the properties of probability distribution, dynamic conditional correlations, and scaling analysis in Dow Jones Industrial Average (DJIA) and Nasdaq intraday returns across 10-min, 30-min, 60-min, 120-min, and 390-min frequencies. The evidence shows that both returns and volatility (standard deviation) increase with the increasing scaling from 10-min to 390-min intervals. By fitting an AR(1)-GARCH(1,1) model to intraday data, we find that AR(1) coefficients are negative for DJIA returns and positive for Nasdaq, exhibiting a positive and negative feedback strategy in DJIA and Nasdaq, respectively. The evidence also shows that these coefficients are statistically significant for either including or excluding opening returns for the 10-min and 30-min frequencies. By examining the dynamic conditional correlation between the DJIA and the Nasdaq across different frequencies, a positive correlation ranging from 0.6 to 0.8 was found. In addition, the variance of the dynamic correlation coefficients is decreasing and appears to be stable for the 2001-2003 period. Finally, both returns on DJIA and Nasdaq satisfy the stable Lévy distributions, implying that both markets can converge to equilibrium by self-governing mechanism after shocks. Results of this work provide relevant implications for investors and policy makers.