Volatility return intervals analysis of the Japanese market

We investigate scaling and memory effects in return intervals between price volatilities above a certain threshold $q$ for the Japanese stock market using daily and intraday data sets. We find that the distribution of return intervals can be approximated by a scaling function that depends only on the ratio between the return interval $\tau$ and its mean $$. We also find memory effects such that a large (or small) return interval follows a large (or small) interval by investigating the conditional distribution and mean return interval. The results are similar to previous studies of other markets and indicate that similar statistical features appear in different financial markets. We also compare our results between the period before and after the big crash at the end of 1989. We find that scaling and memory effects of the return intervals show similar features although the statistical properties of the returns are different.Comment: 11 page

Financial factor influence on scaling and memory of trading volume in stock market

We study the daily trading volume volatility of 17,197 stocks in the U.S. stock markets during the period 1989--2008 and analyze the time return intervals $\tau$ between volume volatilities above a given threshold q. For different thresholds q, the probability density function P_q(\tau) scales with mean interval as P_q(\tau)=^{-1}f(\tau/) and the tails of the scaling function can be well approximated by a power-law f(x)~x^{-\gamma}. We also study the relation between the form of the distribution function P_q(\tau) and several financial factors: stock lifetime, market capitalization, volume, and trading value. We find a systematic tendency of P_q(\tau) associated with these factors, suggesting a multi-scaling feature in the volume return intervals. We analyze the conditional probability P_q(\tau|\tau_0) for $\tau$ following a certain interval \tau_0, and find that P_q(\tau|\tau_0) depends on \tau_0 such that immediately following a short/long return interval a second short/long return interval tends to occur. We also find indications that there is a long-term correlation in the daily volume volatility. We compare our results to those found earlier for price volatility.Comment: 17 pages, 6 figure

Return interval distribution of extreme events and long term memory

The distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines. It is well known that many physical processes in nature and society display long range correlations. Hence, in the last few years, considerable research effort has been directed towards studying the distribution of return intervals for long range correlated time series. Based on numerical simulations, it was shown that the return interval distributions are of stretched exponential type. In this paper, we obtain an analytical expression for the distribution of return intervals in long range correlated time series which holds good when the average return intervals are large. We show that the distribution is actually a product of power law and a stretched exponential form. We also discuss the regimes of validity and perform detailed studies on how the return interval distribution depends on the threshold used to define extreme events.Comment: 8 pages, 6 figure

Scaling and memory of intraday volatility return intervals in stock market

We study the return interval $\tau$ between price volatilities that are above a certain threshold $q$ for 31 intraday datasets, including the Standard & Poor's 500 index and the 30 stocks that form the Dow Jones Industrial index. For different threshold $q$, the probability density function $P_q(\tau)$ scales with the mean interval $\bar{\tau}$ as $P_q(\tau)={\bar{\tau}}^{-1}f(\tau/\bar{\tau})$, similar to that found in daily volatilities. Since the intraday records have significantly more data points compared to the daily records, we could probe for much higher thresholds $q$ and still obtain good statistics. We find that the scaling function $f(x)$ is consistent for all 31 intraday datasets in various time resolutions, and the function is well approximated by the stretched exponential, $f(x)\sim e^{-a x^\gamma}$, with $\gamma=0.38\pm 0.05$ and $a=3.9\pm 0.5$, which indicates the existence of correlations. We analyze the conditional probability distribution $P_q(\tau|\tau_0)$ for $\tau$ following a certain interval $\tau_0$, and find $P_q(\tau|\tau_0)$ depends on $\tau_0$, which demonstrates memory in intraday return intervals. Also, we find that the mean conditional interval $$ increases with $\tau_0$, consistent with the memory found for $P_q(\tau|\tau_0)$. Moreover, we find that return interval records have long term correlations with correlation exponents similar to that of volatility records.Comment: 19 pages, 8 figure

Finite-Size Effects on Return Interval Distributions for Weakest-Link-Scaling Systems

The Weibull distribution is a commonly used model for the strength of brittle materials and earthquake return intervals. Deviations from Weibull scaling, however, have been observed in earthquake return intervals and in the fracture strength of quasi-brittle materials. We investigate weakest-link scaling in finite-size systems and deviations of empirical return interval distributions from the Weibull distribution function. We use the ansatz that the survival probability function of a system with complex interactions among its units can be expressed as the product of the survival probability functions for an ensemble of representative volume elements (RVEs). We show that if the system comprises a finite number of RVEs, it obeys the $\kappa$-Weibull distribution. We conduct statistical analysis of experimental data and simulations that show good agreement with the $\kappa$-Weibull distribution. We show the following: (1) The weakest-link theory for finite-size systems involves the $\kappa$-Weibull distribution. (2) The power-law decline of the $\kappa$-Weibull upper tail can explain deviations from the Weibull scaling observed in return interval data. (3) The hazard rate function of the $\kappa$-Weibull distribution decreases linearly after a waiting time $\tau_c \propto n^{1/m}$, where $m$ is the Weibull modulus and $n$ is the system size in terms of representative volume elements. (4) The $\kappa$-Weibull provides competitive fits to the return interval distributions of seismic data and of avalanches in a fiber bundle model. In conclusion, using theoretical and statistical analysis of real and simulated data, we show that the $\kappa$-Weibull distribution is a useful model for extreme-event return intervals in finite-size systems.Comment: 33 pages, 11 figure

Short-term returns and the predictability of Finnish stock returns

The predictability of Finnish stock returns is studied using the framework of Ferson and Harvey (1993). We use a conditional asset pricing model where risk premia and risk sensitivities are conditioned on a range of financial information variables. In particular, we study the effect of the return interval on the predictability of short-term stock returns. Using daily, weekly, and monthly Finnish size and industry-sorted portfolio returns, we find that the predictability of returns increases with the length of return interval, but so does the power of the conditional pricing model to explain the predictability. Consistent with earlier results, we report that the time variation in risk premium accounts for most of the predictability. However, the results show also there is a sizable positive interaction between beta and risk premium which seems to increase for smaller companies.asset pricing; predictability; return interval; time aggregation