Economy – Quantitative Finance – Statistical Finance
Scientific paper
2007-07-31
Phys. Rev. E 77, 016109 (2008)
Economy
Quantitative Finance
Statistical Finance
19 pages, 6 figures
Scientific paper
10.1103/PhysRevE.77.016109
The distribution of the return intervals $\tau$ between volatilities above a threshold $q$ for financial records has been approximated by a scaling behavior. To explore how accurate is the scaling and therefore understand the underlined non-linear mechanism, we investigate intraday datasets of 500 stocks which consist of the Standard & Poor's 500 index. We show that the cumulative distribution of return intervals has systematic deviations from scaling. We support this finding by studying the m-th moment $\mu_m \equiv <(\tau/<\tau>)^m>^{1/m}$, which show a certain trend with the mean interval $<\tau>$. We generate surrogate records using the Schreiber method, and find that their cumulative distributions almost collapse to a single curve and moments are almost constant for most range of $<\tau>$. Those substantial differences suggest that non-linear correlations in the original volatility sequence account for the deviations from a single scaling law. We also find that the original and surrogate records exhibit slight tendencies for short and long $<\tau>$, due to the discreteness and finite size effects of the records respectively. To avoid as possible those effects for testing the multiscaling behavior, we investigate the moments in the range $10<<\tau>\leq100$, and find the exponent $\alpha$ from the power law fitting $\mu_m\sim<\tau>^\alpha$ has a narrow distribution around $\alpha\neq0$ which depend on m for the 500 stocks. The distribution of $\alpha$ for the surrogate records are very narrow and centered around $\alpha=0$. This suggests that the return interval distribution exhibit multiscaling behavior due to the non-linear correlations in the original volatility.
Havlin Shlomo
Stanley Eugene H.
Wang Fengzhong
Yamasaki Kazuko
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