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This study investigates the time evolution of market efficiency in the Japanese stock markets, considering three indices: Tokyo Stock Price Index (TOPIX), Tokyo Stock Exchange Second Section Index, and TOPIX-Small. The Hurst exponent reveals that the Japanese markets are inefficient in their early stages and improve gradually. TOPIX and TOPIX-Small showed an anti-persistence around the year 2000, which still persists. The degree of multifractality varies over time and does not show that the Japanese markets are permanently efficient. The multifractal properties of the Japanese markets changed considerably around the year 2000; this may have been caused by the complete migration from the stock trading floor to the Tokyo Stock Exchange’s computer trading system and the financial system reform, also known as the “Japanese Big Bang”.

Physicist Professor Tetsuya Takaishi is based at the liberal arts education center, Hiroshima University of Economics in Japan, and is conducting research on a variety of cryptocurrencies. His research is focused on clarifying the mechanism of price fluctuations, in particular answering questions about the volatility inherent in cryptocurrencies, including understanding what affects the price of cryptocurrencies and why the price fluctuates in the way that it does. His chief focus is on cryptocurrencies, specifically Bitcoin, which is the most well-known of the cryptocurrencies. Takaishi's latest project is investigating the statistical nature of Bitcoin price fluctuations.

This letter investigates the dynamic relationship between market efficiency, liquidity, and multifractality of Bitcoin. We find that before 2013 liquidity is low and the Hurst exponent is less than 0.5, indicating that the Bitcoin time series is anti-persistent. After 2013, as liquidity increased, the Hurst exponent rose to approximately 0.5, improving market efficiency. For several periods, however, the Hurst exponent was found to be significantly less than 0.5, making the time series anti-persistent during those periods. We also investigate the multifractal degree of the Bitcoin time series using the generalized Hurst exponent and find that the multifractal degree is related to market efficiency in a non-linear manner., Comment: 10 pages, 6 figures

While relevant stylized facts are observed for Bitcoin markets, we find a distinct property for the scaling behavior of the cumulative return distribution. For various assets, the tail index $\mu$ of the cumulative return distribution exhibits $\mu \approx 3$, which is referred to as "the inverse cubic law." On the other hand, that of the Bitcoin return is claimed to be $\mu \approx 2$, which is known as "the inverse square law." We investigate the scaling properties using recent Bitcoin data and find that the tail index changes to $\mu \approx 3$, which is consistent with the inverse cubic law. This suggests that some properties of the Bitcoin market could vary over time. We also investigate the autocorrelation of absolute returns and find that it is described by a power-law with two scaling exponents. By analyzing the absolute returns standardized by the realized volatility, we verify that the Bitcoin return time series is consistent with normal random variables with time-varying volatility., Comment: 6 pages, 3 figures

The realized stochastic volatility model has been introduced to estimate more accurate volatility by using both daily returns and realized volatility. The main advantage of the model is that no special bias-correction factor for the realized volatility is required a priori. Instead, the model introduces a bias-correction parameter responsible for the bias hidden in realized volatility. We empirically investigate the bias-correction parameter for realized volatilities calculated at various sampling frequencies for six stocks on the Tokyo Stock Exchange, and then show that the dynamic behavior of the bias-correction parameter as a function of sampling frequency is qualitatively similar to that of the Hansen–Lunde bias-correction factor although their values are substantially different. Under the stochastic diffusion assumption of the return dynamics, we investigate the accuracy of estimated volatilities by examining the standardized returns. We find that while the moments of the standardized returns from low-frequency realized volatilities are consistent with the expectation from the Gaussian variables, the deviation from the expectation becomes considerably large at high frequencies. This indicates that the realized stochastic volatility model itself cannot completely remove bias at high frequencies.

We propose a new ARCH-type model that uses a rational function to capture the asymmetric response of volatility to returns, known as the “leverage effect”. Using 10 individual stocks on the Tokyo Stock Exchange and two stock indices, we compare the new model with several other asymmetric ARCH-type models. We find that according to the deviance information criterion, the new model ranks first for several stocks. Results show that the proposed new model can be used as an alternative asymmetric ARCH-type model in empirical applications.

This letter investigates the Taylor effect in Bitcoin time series. It is found that the Taylor effect exists in Bitcoin, and the value of the power that maximizes the autocorrelation of the power of absolute returns depends on a time lag in the autocorrelation function. While the Taylor effect of foreign exchange rates has a daily seasonality, we could not find any daily seasonality in the Taylor effect of Bitcoin.

Recent studies have found that the log-volatility of asset returns exhibit roughness. This study investigates roughness or the anti-persistence of Bitcoin volatility. Using the multifractal detrended fluctuation analysis, we obtain the generalized Hurst exponent of the log-volatility increments and find that the generalized Hurst exponent is less than $1/2$, which indicates log-volatility increments that are rough. Furthermore, we find that the generalized Hurst exponent is not constant. This observation indicates that the log-volatility has multifractal property. Using shuffled time series of the log-volatility increments, we infer that the source of multifractality partly comes from the distributional property., Comment: 12 pages, 8 figures

Using an Ising-based model extended to simulate multiple stock time series, we perform a large-scale simulation for a financial system with 100 stocks. We find that the financial system shows fat-tailed return distributions and the system volatility level measured as an average of absolute-returns changes over time. We investigate the dynamical properties of cross-correlation matrices among stocks and find that the eigenvalue distributions of the cross-correlation matrices deviate from those of the random matrix theory. It is found that the cumulative risk fraction (CRF) constructed from the largest eigenvalues changes at periods where the volatility level is high. The inverse participation ratio (IPR) and its higher-power version, IPR6, also exhibit the changes at the same high volatility periods. Therefore, the CRF, IPR, and IPR6 are expected to be useful measurements to identify abnormal states such as high-volatility periods.

We study the asymmetric multifractality between five main cryptocurrencies (Bitcoin, Litecoin, Ripple, Monero, and Dash) and six equity ETFs from February 2, 2015 to April 30, 2019. The equity ETFs selected relate to emerging markets, China, Japan, the energy sector, financial sector, and technology–Nasdaq. Results from the multifractal asymmetric detrended cross-correlation analysis show a significant persistence and evidence of asymmetric multifractality in the cross-correlation between most of the pairs of cryptocurrencies and ETFs. These findings, which are consistent with previous findings on the susceptibility of Bitcoin to multifractality, indicate the presence of heterogeneity in the cross-relationship between most cryptocurrencies and equity ETFs.

This paper investigates the return-volatility asymmetry of Bitcoin. We find that the cross correlations between return and volatility (squared return) are mostly insignificant on a daily level. In the high-frequency region, we find thata power-law appears in negative cross correlation between returns and future volatilities, which suggests that the cross correlation is \revision{long ranged}. We also calculate a cross correlation between returns and the power of absolute returns, and we find that the strength of \revision{the cross correlations} depends on the value of the power., Comment: 10 pages, 5 figures

We study the (de)localization phenomena of one-component lattice fermions in spin backgrounds. The O(3) classical spin variables on sites fluctuate thermally through the ordinary nearest-neighbor coupling. Their complex two-component (CP$^1$-Schwinger boson) representation forms a composite U(1) gauge field on bond, which acts on fermions as a fluctuating hopping amplitude in a gauge invariant manner. For the case of antiferromagnetic (AF) spin coupling, the model has close relationship with the $t$-$J$ model of strongly-correlated electron systems. We measure the unfolded level spacing distribution of fermion energy eigenvalues and the participation ratio of energy eigenstates. The results for AF spin couplings suggest a possibility that, in two dimensions, all the energy eigenstates are localized. In three dimensions, we find that there exists a mobility edge, and estimate the critical temperature $T_{\ss LD}(\delta)$ of the localization-delocalization transition at the fermion concentration $\delta$., Comment: Version to appear in Phys. Rev. B

We perform a large-scale simulation of an Ising-based financial market model that includes 300 asset time series. The financial system simulated by the model shows a fat-tailed return distribution and volatility clustering and exhibits unstable periods indicated by the volatility index measured as the average of absolute-returns. Moreover, we determine that the cumulative risk fraction, which measures the system risk, changes at high volatility periods. We also calculate the inverse participation ratio (IPR) and its higher-power version, IPR6, from the absolute-return cross-correlation matrix. Finally, we show that the IPR and IPR6 also change at high volatility periods., Comment: 10 pages, 9 figures

Using 1-min returns of Bitcoin prices, we investigate statistical properties and multifractality of a Bitcoin time series. We find that the 1-min return distribution is fat-tailed, and kurtosis largely deviates from the Gaussian expectation. Although for large sampling periods, kurtosis is anticipated to approach the Gaussian expectation, we find that convergence to that is very slow. Skewness is found to be negative at time scales shorter than one day and becomes consistent with zero at time scales longer than about one week. We also investigate daily volatility-asymmetry by using GARCH, GJR, and RGARCH models, and find no evidence of it. On exploring multifractality using multifractal detrended fluctuation analysis, we find that the Bitcoin time series exhibits multifractality. The sources of multifractality are investigated, confirming that both temporal correlation and the fat-tailed distribution contribute to it. The influence of "Brexit" on June 23, 2016 to GBP--USD exchange rate and Bitcoin is examined in multifractal properties. We find that, while Brexit influenced the GBP--USD exchange rate, Bitcoin was robust to Brexit., 19 pages, 9 figures

We calculate realized volatility of the Nikkei Stock Average (Nikkei225) Index on the Tokyo Stock Exchange and investigate the return dynamics. To avoid the bias on the realized volatility from the non-trading hours issue we calculate realized volatility separately in the two trading sessions, i.e. morning and afternoon, of the Tokyo Stock Exchange and find that the microstructure noise decreases the realized volatility at small sampling frequency. Using realized volatility as a proxy of the integrated volatility we standardize returns in the morning and afternoon sessions and investigate the normality of the standardized returns by calculating variance, kurtosis and 6th moment. We find that variance, kurtosis and 6th moment are consistent with those of the standard normal distribution, which indicates that the return dynamics of the Nikkei Stock Average are well described by a Gaussian random process with time-varying volatility., Comment: 9 pages, 7 figures

In this paper we propose an Ising model which simulates multiple financial time series. Our model introduces the interaction which couples to spins of other systems. Simulations from our model show that time series exhibit the volatility clustering that is often observed in the real financial markets. Furthermore we also find non-zero cross correlations between the volatilities from our model. Thus our model can simulate stock markets where volatilities of stocks are mutually correlated., 4 pages, 4 figures

Seismic noise includes the information that comes from crust of earth and hypocenter. The study of seismic noise is an essential topic for earthquake predictability and investigation of crustal structure. In this paper we analyze the seismic noise from 46 stations in all around Japan of Full Range Seismograph Network of Japan (F-net). To investigate the influence from earthquake we analyze two types of seismic noise data, one is the data after earthquake shake, which from 2,000 seconds after the max shake of an earthquake, and others are without any earthquake effects. We find that (i) the magnitude of seismic noise values follows a log-normal distribution and (ii) the conditional mean growth rate and the standard deviation of the growth rate of the magnitude value both obey power-law with the magnitude value. Furthermore we also find that the Hurst exponent depends on the max amplitude of earthquake, and shows a linear correlation with logarithmic max amplitude.

We analyze the realized volatility of stocks traded on the Tokyo Stock Exchange using 5-min high-frequency stock prices. We find that the distributions of stock returns standardized by the realized volatility are consistent with Gaussian distributions which enable us to view the system in superstatistics. Our results suggest that the distributions of the realized volatility are explained with inverse gamma distributions.

We calculate the realized volatility in the spin model of financial markets and examine the returns standardized by the realized volatility. We find that moments of the standardized returns agree with the theoretical values of standard normal variables. This is the first evidence that the return dynamics of the spin financial market is consistent with the view of the mixture-of-distribution hypothesis that also holds in the real financial markets., 4 pages, 5 figures

In this paper we investigate an Ising model which simulates multiple financial time series. The model is called the multiple time series Ising model that introduces the interaction which couples to spins of other systems. We analyze the return time series data simulated by the model and find that several stylized facts such as volatility clustering appear in the model. Non-zero cross correlations between the absolute returns are also present in the model. On the other hand no cross correlations between returns are observed. We also estimate volatility of the return time series by the GARCH model and check the view of the finite-variance mixture of normal distributions for the return data by using the GARCH volatility. The results are found to be consistent with this veiw.

Firm size data usually do not show the normality that is often assumed in statistical analysis such as regression analysis. In this study we focus on two firm size data: the number of employees and sale. Those data deviate considerably from a normal distribution. To improve the normality of those data we transform them by the Box-Cox transformation with appropriate parameters. The Box-Cox transformation parameters are determined so that the transformed data best show the kurtosis of a normal distribution. It is found that the two firm size data transformed by the Box-Cox transformation show strong linearity. This indicates that the number of employees and sale have the similar property as a firm size indicator. The Box-Cox parameters obtained for the firm size data are found to be very close to zero. In this case the Box-Cox transformations are approximately a log-transformation. This suggests that the firm size data we used are approximately log-normal distributions., Comment: 4 pages, 9 figures

We report on three topics on finite density simulations: (i) the derivative method for hadronic quantities, (ii) phase fluctuations in the vicinity of the critical temperature and (iii) the density of states method at finite isospin density., 11 pages, 11 figures, talk given at Finite Density QCD, at Nara, Japan 10-12 July 2003

This is a pedagogical review of the lattice study of finite density QCD, which is intended to provide the minimum necessary contents, so that the paper may be used as the first reading for a newcomer to the field and also for those working in nonlattice communities. After a brief introduction to argue why finite density QCD can be a new attractive subject, we describe fundamental formulae which are necessary for the following sections. Then we survey lattice QCD simulations in small chemical potential regions, where several prominent works have been reported recently. Next, two-color QCD calculations are discussed, where we have a chance to glance at many new features of finite density QCD, and indeed recent simulations indicated quark pair condensation and the in-medium effect. Tables of SU(3) and SU(2) lattice simulations at finite baryon density are given. In the next section, we make a survey of several related works which may be a starting point of the new development in the future, although some works do not attract much attention now. Materials are described in a pedagogical manner. Starting from a simple 2-d model, we briefly discuss a lattice analysis of NJL model. We describe a non-perturbative analytical approach, i.e., strong coupling approximation method and some results. Canonical ensemble approach instead of usual grand canonical ensample may be another route to reach high density. We examine the density of state method and show this old idea includes recently proposed factorization method. An alternative method, complex Langevin equation and an interesting model, finite isospin model, are also discussed. In Appendix, we give several technical points which are useful in practical calculations., 50 pages, 43 Postscript figures, submitted to Prog. Theor. Phys, uses ptptex.cls and wrapft.sty

We analyse temporal and spatial meson correlators in quenched lattice QCD at T| > 0. Above T c we find different (temporal) pole masses and (spatial) screening masses, signals of plasma formation and indication of persisting mesonic excitations.

A spin model is used for simulations of financial markets. To determine return volatility in the spin financial market we use the GARCH model often used for volatility estimation in empirical finance. We apply the Bayesian inference performed by the Markov Chain Monte Carlo method to the parameter estimation of the GARCH model. It is found that volatility determined by the GARCH model exhibits "volatility clustering" also observed in the real financial markets. Using volatility determined by the GARCH model we examine the mixture-of-distribution hypothesis (MDH) suggested for the asset return dynamics. We find that the returns standardized by volatility are approximately standard normal random variables. Moreover we find that the absolute standardized returns show no significant autocorrelation. These findings are consistent with the view of the MDH for the return dynamics., 10 pages

Measuring volatility in financial markets is a primary challenge in the theory and practice of risk management and is essential when developing investment strategies. Although the vast literature on the topic describes many different models, two nonparametric measurements have emerged and received wide use over the past decade: realized volatility and absolute return volatility. The former is strongly favored in the financial sector and the latter by econophysicists. We examine the memory and clustering features of these two methods and find that both enable strong predictions. We compare the two in detail and find that although realized volatility has a better short-term effect that allows predictions of near-future market behavior, absolute return volatility is easier to calculate and, as a risk indicator, has approximately the same sensitivity as realized volatility. Our detailed empirical analysis yields valuable guidelines for both researchers and market participants because it provides a significantly clearer comparison of the strengths and weaknesses of the two methods.

Simulations of odd flavors QCD can be performed in the framework of the hybrid Monte Carlo algorithm where the inverse of the fermion matrix is approximated by a polynomial. In this exploratory study we perform three flavors QCD simulations. We make a comparison of the hybrid Monte Carlo algorithm and the R-algorithm which also simulates odd flavors systems but has step-size errors. We find that results from our hybrid Monte Carlo algorithm are in agreement with those from the R-algorithm obtained at very small step-size., Comment: Lattice 2000 (Algorithms), 5 pages, 8 figures, LaTeX

The stochastic volatility model is one of volatility models which infer latent volatility of asset returns. The Bayesian inference of the stochastic volatility (SV) model is performed by the hybrid Monte Carlo (HMC) algorithm which is superior to other Markov Chain Monte Carlo methods in sampling volatility variables. We perform the HMC simulations of the SV model for two liquid stock returns traded on the Tokyo Stock Exchange and measure the volatilities of those stock returns. Then we calculate the accuracy of the volatility measurement using the realized volatility as a proxy of the true volatility and compare the SV model with the GARCH model which is one of other volatility models. Using the accuracy calculated with the realized volatility we find that empirically the SV model performs better than the GARCH model., Comment: 10 pages, 5 figures

We analyze realized volatilities constructed using high-frequency stock data on the Tokyo Stock Exchange. In order to avoid non-trading hours issue in volatility calculations we define two realized volatilities calculated separately in the two trading sessions of the Tokyo Stock Exchange, i.e. morning and afternoon sessions. After calculating the realized volatilities at various sampling frequencies we evaluate the bias from the microstructure noise as a function of sampling frequency. Taking into account of the bias to realized volatility we examine returns standardized by realized volatilities and confirm that price returns on the Tokyo Stock Exchange are described approximately by Gaussian time series with time-varying volatility, i.e. consistent with a mixture of distributions hypothesis., Comment: 12 pages, reference corrected

The results of meson and baryon spectroscopy composed of charm and strange quarks are reported by the use of quenched Wilson fermions on a 323 x 48 lattice at β = 6.3. Ground state hadrons composed of two or three quarks with different hopping parameters, in a region κ = 0.13 to 0.15, are measured. It is found that their masses are well described by a quadratic polynomial in terms of multi-1/κ variables in this region. Adjusting vector meson mass ratios between (ss), (sc) and (cc), the hopping parameters of strange quark and charm quark are determined to be κs = 0.14999(22) and κc = 0.13548(82) without chiral extrapolation. Masses of not yet observed ssc, scc and ccc baryons in GeV are estimated to be 2.778 ± 0.0]6 (ssc), 3.858 ± 0.015 (scc) for (12)+ and 2.813 ± 0.167 (ssc), 3.869 ± 0.055 (scc) 4.880 ± 0.017 (ccc) for (3/2)+. As for the meson spin splitting structure, the quenched Wilson spectrum is more degenerate in comparison with real hadrons, as already pointed out by many authors.

We study the deconfinement transition of $N_f=1$ QCD by the hybrid Monte Carlo algorithm with Wilson fermions. We calculate the Polyakov loop, its susceptibility and Binder cumulant and use the $\chi^2$ method to locate the phase transition point. Our results are similar to the previous results obtained by the multiboson algorithm., Comment: 3 pages, 3 figures: Lattice2003(Non-zero temperature and density)

A parallelization study of Quantum Chromodynamics (QCD) simulation on a non-dedicated MIMD computer, Fujitsu AP1000, is reported. The AP1000 is a highly parallel computer with distributed memory. Data communication is fast not only among the nearest neighbor processing units, but also between widely separated ones. We study SU(3) quenched QCD simulation with lattice sizes of 324 and 323 × 48, on the 512-processor AP1000, and report parallelization techniques and physical results for a renormalization group study and hadron spectroscopy. The AP1000 is efficient for these QCD simulations and shows good performance. A bottleneck occurs in the current simulation as data is passed to the front-end processor for storage.

We study stock market instability by using cross-correlations constructed from the return time series of 366 stocks traded on the Tokyo Stock Exchange from January 5, 1998 to December 30, 2013. To investigate the dynamical evolution of the cross-correlations, cross-correlation matrices are calculated with a rolling window of 400 days. To quantify the volatile market stages where the potential risk is high, we apply the principal components analysis and measure the cumulative risk fraction (CRF), which is the system variance associated with the first few principal components. From the CRF, we detected three volatile market stages corresponding to the bankruptcy of Lehman Brothers, the 2011 Tohoku Region Pacific Coast Earthquake, and the FRB QE3 reduction observation in the study period. We further apply the random matrix theory for the risk analysis and find that the first eigenvector is more equally de-localized when the market is volatile., Comment: 5 pages, 4 figures

The demon method is applied to determine the effective action on blocked SU(3) gauge configurations. First the method is tested on SU(3) gauge configurations with known couplings. It turns out that the method works well to determine couplings with good precision in rather short microcanonical updates. Next the method is implemented for a set of blocked SU(3) gauge configurations and we successfully determine an effective action in seven-dimensional coupling constant space.

We study the autocorrelation time of blocked loops on 8 4 , 16 4 and 32 4 lattices in pure SU(3) lattice gauge theory over a wide range of β (= 6/ g 2 ) with high statistics. The critical exponent of integrated autocorrelation time by hybrid overrelaxation updating with fixed mixing ratio is found to be 1.74 ± 0.06. This suggests that the overrelaxation still suffer from critical slowing down toward the continuum limit.

We present very precise results from the MCRG analysis on large lattices performed in the frame of the QCD-TARO collaboration using the highly parallel computer AP1000 of Fujitsu. We find good scaling behavior of pure SU(3) theory with strong non-perturbative effects in the range 6 β