Scaling and memory effect in volatility return interval of the Chinese stock market

Abstract

We investigate the probability distribution of the volatility return intervals τ for the Chinese stock market. We rescale both the probability distribution P q (τ ) and the volatility return intervals τ as P q (τ ) = 1/τ f (τ /τ ) to obtain a uniform scaling curve for different threshold value q. The scaling curve can be well fitted by the stretched exponential function f (x) ∼ e −αx γ , which suggests memory exists in τ . To demonstrate the memory effect, we investigate the conditional probability distribution P q (τ |τ 0 ), the mean conditional interval τ |τ 0 and the cumulative probability distribution of the cluster size of τ . The results show clear clustering effect. We further investigate the persistence probability distribution P ± (t) and find that P − (t) decays by a power law with the exponent far different from the value 0.5 for the random walk, which further confirms long memory exists in τ . The scaling and long memory effect of τ for the Chinese stock market are similar to those obtained from the United States and the Japanese financial markets.

Early warning of large volatilities based on recurrence interval analysis in Chinese stock markets

“…It has been found that the recurrence interval distribution above a fixed threshold has a power-law tail for the daily volatilities in Japanese market [13,26], the minute-by-minute volatilities in Korean market [27] and Italian market [28], the daily returns in US stock markets [3,16,17], the minute-by-minute returns in Chinese markets [18], and the minute-by-minute trading volume in US markets [25] and Chinese markets [24]. A number of studies ranging from daily to high-frequency data and from developed to emerging markets [14,[29][30][31][32][33][34][35][36], have also reported that the distribution of the recurrence intervals of financial volatility is a stretched exponential. Reference [22] reports that in Chinese markets the recurrence time between returns above a given positive threshold or below a negative threshold for the index spot and futures fits a stretched exponential distribution.…”

Geography and distance effect on financial dynamics in the Chinese stock market

“…Among them, a lot of physicists devoted to the study of financial dynamics in the past two decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14], and some stylized facts have been revealed from the statistical physics perspective. Scaling behavior of the return and return interval distributions has been observed for different markets [1][2][3][4][15][16][17][18]. Volatility clustering is found to be universal for most markets [3,19].…”

Spatial and temporal structures of four financial markets in Greater China

“…From a volume volatility time series, we may extract the recurrence intervals τ between consecutive volatilities above a threshold q, and construct a series of the recurrence intervals {τ (q)} [26,27,28,29]. The threshold q is measured in unit of the standard deviation of the volume volatility.…”

“…The analysis of the recurrence interval may deepen the understanding of the dynamic behavior in financial markets [21,25]. Recently, statistical properties of the recurrence intervals of volume volatilities and price volatilities have been studied [26,27,28,29]. We present a comparative study on the recurrence interval distributions of the four stock markets.…”