Statistical Properties, Dynamic Conditional Correlation, Scaling Analysis of High-Frequency Intraday Stock Returns: Evidence from Dow-Jones and Nasdaq Indices

This paper investigates statistical properties of high-frequency intraday stock returns across various frequencies. Both time series and panel data are employed to explore probability distribution properties, autocorrelations, dynamic conditional correlations, and scaling analysis in the Dow Jones Industrial Average (DJIA) and the NASDAQ intraday returns across 10-minute, 30-monute, 60-minute, 120-minute, and 390-minute frequencies from August 1, 1997, to December 31, 2003. The evidence shows that all of the statistical estimates are highly influenced by the opening returns that contain overnight and non-regular information. The stylized fact of high opening returns generates significant negative (in DJIA) and positive (in NASDAQ) autocorrelations. After excluding the opening intervals, DJIA exhibits a pattern similar to a random walk. While examining the AR(1)-GARCH (1, 1) pattern across both time and frequency variants, we find consistent negative AR(1) at 10-minute and 30-minute frequencies in the DJIA, positive AR(1) in the NASDAQ intraday returns, and no obvious pattern beyond the 30-minute intraday return series. By examining the dynamic conditional correlation coefficients between the DJIA and the NASDAQ at different frequencies, we find that the correlations are positive and fluctuate mainly in the range of 0.6 to 0.8. The variance of the correlation coefficients has been declining and appears to be stable for the post-2001 period. We then check the conditions for a stable Levy distribution and find both the DJIA and the NASDAQ can converge to their systematic equilibriums after shocks, implying both systems are characterized by a self-stabilizing mechanism.

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