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

Effect of various dopant elements on primary graphite growth

Five spheroidal graphite cast irons were investigated, a usual ferritic grade and four pearlitic alloys containing Cu and doped with Sb, Sn and Ti. These alloys were remelted in a graphite crucible, leading to volatilization of the magnesium added for spheroidization and to carbon saturation of the liquid. The alloys were then cooled down and maintained at a temperature above the eutectic temperature. During this step, primary graphite could develop showing various features depending on the doping elements added. The largest effects were that of Ti which greatly reduces graphite nucleation and growth, and that of Sb which leads to rounded agglomerates instead of lamellar graphite. The samples have been investigated with secondary ion mass spectrometry to enlighten distribution of elements in primary graphite. SIMS analysis showed almost even distribution of elements, including Mg and Al (from the inoculant) in the ferritic grade, while uneven distribution was evident in all doped alloys. Investigations are going on to clarify if the uneven distribution is associated with structural defects in the graphite precipitates

Scaling of the distribution of fluctuations of financial market indices

We study the distribution of fluctuations over a time scale $\Delta t$ (i.e., the returns) of the S&P 500 index by analyzing three distinct databases. Database (i) contains approximately 1 million records sampled at 1 min intervals for the 13-year period 1984-1996, database (ii) contains 8686 daily records for the 35-year period 1962-1996, and database (iii) contains 852 monthly records for the 71-year period 1926-1996. We compute the probability distributions of returns over a time scale $\Delta t$, where $\Delta t$ varies approximately over a factor of 10^4 - from 1 min up to more than 1 month. We find that the distributions for $\Delta t \leq$ 4 days (1560 mins) are consistent with a power-law asymptotic behavior, characterized by an exponent $\alpha \approx 3$, well outside the stable L\'evy regime $0 < \alpha < 2$. To test the robustness of the S&P result, we perform a parallel analysis on two other financial market indices. Database (iv) contains 3560 daily records of the NIKKEI index for the 14-year period 1984-97, and database (v) contains 4649 daily records of the Hang-Seng index for the 18-year period 1980-97. We find estimates of $\alpha$ consistent with those describing the distribution of S&P 500 daily-returns. One possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility. For time scales longer than $(\Delta t)_{\times} \approx 4$ days, our results are consistent with slow convergence to Gaussian behavior.Comment: 12 pages in multicol LaTeX format with 27 postscript figures (Submitted to PRE May 20, 1999). See http://polymer.bu.edu/~amaral/Professional.html for more of our work on this are

Statistical Properties of Share Volume Traded in Financial Markets

We quantitatively investigate the ideas behind the often-expressed adage `it takes volume to move stock prices', and study the statistical properties of the number of shares traded $Q_{\Delta t}$ for a given stock in a fixed time interval $\Delta t$. We analyze transaction data for the largest 1000 stocks for the two-year period 1994-95, using a database that records every transaction for all securities in three major US stock markets. We find that the distribution $P(Q_{\Delta t})$ displays a power-law decay, and that the time correlations in $Q_{\Delta t}$ display long-range persistence. Further, we investigate the relation between $Q_{\Delta t}$ and the number of transactions $N_{\Delta t}$ in a time interval $\Delta t$, and find that the long-range correlations in $Q_{\Delta t}$ are largely due to those of $N_{\Delta t}$. Our results are consistent with the interpretation that the large equal-time correlation previously found between $Q_{\Delta t}$ and the absolute value of price change $| G_{\Delta t} |$ (related to volatility) are largely due to $N_{\Delta t}$.Comment: 4 pages, two-column format, four figure

Investigation of Cu poor and Cu rich Cu In,Ga Se2 CdS interfaces using hard X ray photoelectron spectroscopy

Cu poor and Cu rich Cu In,Ga Se2 CIGSe absorbers were used as substrates for the chemical bath deposition of ultrathin CdS buffer layers in the thickness range of a few nanometers in order to make the CIGSe CdS interface accessible by hard X ray photo emission spectroscopy. The composition of both, the absorber and the buffer layer as well as the energetics of the interface was investigated at room temperature and after heating the samples to elevated temperatures 200 C, 300 C and 400 C . It was found that the amount of Cd after the heating treatment depends on the near surface composition of the CIGSe absorber. No Cd was detected on the Cu poor surface after the 400 C treatment due to its diffusion into the CIGSe layer. In contrast, Cd was still present on the Cu rich surface after the same treatment at 400

Statistical Properties of Cross-Correlation in the Korean Stock Market

We investigate the statistical properties of the correlation matrix between individual stocks traded in the Korean stock market using the random matrix theory (RMT) and observe how these affect the portfolio weights in the Markowitz portfolio theory. We find that the distribution of the correlation matrix is positively skewed and changes over time. We find that the eigenvalue distribution of original correlation matrix deviates from the eigenvalues predicted by the RMT, and the largest eigenvalue is 52 times larger than the maximum value among the eigenvalues predicted by the RMT. The $\beta_{473}$ coefficient, which reflect the largest eigenvalue property, is 0.8, while one of the eigenvalues in the RMT is approximately zero. Notably, we show that the entropy function $E(\sigma)$ with the portfolio risk $\sigma$ for the original and filtered correlation matrices are consistent with a power-law function, $E(\sigma) \sim \sigma^{-\gamma}$, with the exponent $\gamma \sim 2.92$ and those for Asian currency crisis decreases significantly

Diagnosing the Clumpy Protoplanetary Disk of the UXor Type Young Star GM Cephei

UX Orionis stars (UXors) are Herbig Ae/Be or T Tauri stars exhibiting sporadic occultation of stellar light by circumstellar dust. GM\,Cephei is such a UXor in the young ($\sim4$~Myr) open cluster Trumpler\,37, showing prominent infrared excess, emission-line spectra, and flare activity. Our photometric monitoring (2008--2018) detects (1)~an $\sim$3.43~day period, likely arising from rotational modulation by surface starspots, (2)~sporadic brightening on time scales of days due to accretion, (3)~irregular minor flux drops due to circumstellar dust extinction, and (4)~major flux drops, each lasting for a couple of months with a recurrence time, though not exactly periodic, of about two years. The star experiences normal reddening by large grains, i.e., redder when dimmer, but exhibits an unusual "blueing" phenomenon in that the star turns blue near brightness minima. The maximum extinction during relatively short (lasting $\leq 50$~days) events, is proportional to the duration, a consequence of varying clump sizes. For longer events, the extinction is independent of duration, suggestive of a transverse string distribution of clumps. Polarization monitoring indicates an optical polarization varying $\sim3\%$--8$\%$, with the level anticorrelated with the slow brightness change. Temporal variation of the unpolarized and polarized light sets constraints on the size and orbital distance of the circumstellar clumps in the interplay with the young star and scattering envelope. These transiting clumps are edge-on manifestations of the ring- or spiral-like structures found recently in young stars with imaging in infrared of scattered light, or in submillimeter of thermalized dust emission.Comment: 20 pages, 9 figure