Correlations and fluctuations in phase coarsening

Wang, K. G.; Glicksman, M.E.; Lou, Chaogang

doi:10.1103/physreve.73.061502

Cited by 30 publications

(39 citation statements)

References 28 publications

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“…The temporal structure in volatilities is complex and still regarded as an open problem. Return interval τ , also called recurrence time or interspike interval, which is the time interval between two consecutive volatilities above a certain threshold q, provides a new approach to analyze long-term correlated time series [13,14,15,16,17,18,19,20,21,22,23,24]. Recent studies on financial markets [17,18,19,20,21] show that, for both daily and intraday data, i) the distribution of scaled interval τ / τ can be approximated by a single scaling function, where τ is the average of τ .…”

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confidence: 99%

“…For financial markets, the PDF of τ , P q (τ ), is well-approximated by the scaling function [17,18],…”

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confidence: 99%

“…From tick prices we set the closest one to a minute mark as the price at that minute. The volatility is defined the same as in Ref [18]. First, we compute the absolute value of the logarithmic change of the minute price, then remove the intraday U-shape pattern, and finally normalize the series with its standard deviation.…”

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confidence: 99%

“…The difference in γ between small and large thresholds suggests multiscaling in the distribution for the whole range. The volatility time series has long-term correlations, which can be characterized by the exponent α obtained from Detrended Fluctuation Analysis (DFA) method [8,17,18,32]. Assuming the validity of the relation between γ in Eq.…”

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confidence: 99%

“…Nevertheless, it characterizes the magnitude of fluctuations and therefore the risk. To avoid the intraday pattern [8,18], we calculate the return on a daily basis. The return is the logarithmic daily price change averaged over the two-year period (2001)(2002), which varies from −0.008 to 0.004 for the 1137 stocks.…”

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confidence: 99%

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Multifactor analysis of multiscaling in volatility return intervals

et al. 2009

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We study the volatility time series of 1137 most traded stocks in the US stock markets for the two-year period 2001-02 and analyze their return intervals τ , which are time intervals between volatilities above a given threshold q. We explore the probability density function of τ , P q (τ ), assuming a stretched exponential function, P q (τ ) ∼ e −τ γ . We find that the exponent γ depends on the threshold in the range between q = 1 and 6 standard deviations of the volatility. This finding supports the multiscaling nature of the return interval distribution. To better understand the multiscaling origin, we study how γ depends on four essential factors, capitalization, risk, number of trades and return. We show that γ depends on the capitalization, risk and return but almost does not depend on the number of trades. This suggests that γ relates to the portfolio selection but not on the market activity. To further characterize the multiscaling of individual stocks, we fit the moments of τ , µ m ≡ (τ / τ ) m 1/m , in the range of 10 < τ ≤ 100 by a power-law, µ m ∼ τ δ . The exponent δ is found also to depend on the capitalization, risk and return but not on the number of trades, and its tendency is opposite to that of γ. Moreover, we show that δ decreases with γ approximately by a linear relation. The return intervals demonstrate the temporal structure of volatilities and our findings suggest that their multiscaling features may be helpful for portfolio optimization.

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