arXiv subjects

Tetsuya Takaishi

Publications and source records attributed to Tetsuya Takaishi.

At least 37 records · Page 2Linked to original sources

arXiv2015

Box-Cox transformation of firm size data in statistical analysis

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.

stat.AP↗

arXiv2014

Analysis of Spin Financial Market by GARCH Model

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.

q-fin.CP↗

arXiv2014

Bayesian estimation of realized stochastic volatility model by Hybrid Monte Carlo algorithm

The hybrid Monte Carlo algorithm (HMCA) is applied for Bayesian parameter estimation of the realized stochastic volatility (RSV) model. Using the 2nd order minimum norm integrator (2MNI) for the molecular dynamics (MD) simulation in the HMCA, we find that the 2MNI is more efficient than the conventional leapfrog integrator. We also find that the autocorrelation time of the volatility variables sampled by the HMCA is very short. Thus it is concluded that the HMCA with the 2MNI is an efficient algorithm for parameter estimations of the RSV model.

q-fin.CP↗

arXiv2013

Empirical Study of the GARCH model with Rational Errors

We use the GARCH model with a fat-tailed error distribution described by a rational function and apply it for the stock price data on the Tokyo Stock Exchange. To determine the model parameters we perform the Bayesian inference to the model. The Bayesian inference is implemented by the Metropolis-Hastings algorithm with an adaptive multi-dimensional Student's t-proposal density. In order to compare the model with the GARCH model with the standard normal errors we calculate information criterions: AIC and DIC, and find that both criterions favor the GARCH model with a rational error distribution. We also calculate the accuracy of the volatility by using the realized volatility and find that a good accuracy is obtained for the GARCH model with a rational error distribution. Thus we conclude that the GARCH model with a rational error distribution is superior to the GARCH model with the normal errors and it can be used as an alternative GARCH model to those with other fat-tailed distributions.

q-fin.CP↗

arXiv2013

Empirical Analysis of Stochastic Volatility Model by Hybrid Monte Carlo Algorithm

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.

q-fin.CP↗

arXiv2013

Analysis of Realized Volatility in Two Trading Sessions of the Japanese Stock Market

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.

q-fin.ST↗

arXiv2010

Bayesian estimation of GARCH model with an adaptive proposal density

A Bayesian estimation of a GARCH model is performed for US Dollar/Japanese Yen exchange rate by the Metropolis-Hastings algorithm with a proposal density given by the adaptive construction scheme. In the adaptive construction scheme the proposal density is assumed to take a form of a multivariate Student's t-distribution and its parameters are evaluated by using the sampled data and updated adaptively during Markov Chain Monte Carlo simulations. We find that the autocorrelation times between the data sampled by the adaptive construction scheme are considerably reduced. We conclude that the adaptive construction scheme works efficiently for the Bayesian inference of the GARCH model.

q-fin.ST↗

arXiv2010

Equation of State at Finite Density from Imaginary Chemical Potential

We perform two flavor QCD simulations with an imaginary chemical potential and measure derivatives of the pressure up to 4th order as a function of the imaginary chemical potential and the temperature $T \in [0.83 T_c, 2 T_c]$. For temperatures $T \geq T_c$, these derivatives are fitted by a Taylor series in $μ/T$ about $μ=0$. A fit limited to 4th order describes the data poorly at all temperatures, showing that we are sensitive to 6th order contributions. Similarly, a 6th order fit fails for temperatures $T_c \leq T \leq 1.05 T_c$, showing the need for 8th order terms. Thus, our method may offer a computational advantage over the direct measurement of Taylor coefficients at $μ=0$. At temperatures $T \leq T_c$, we fit our data with a hadron resonance gas ansatz. The fit starts to fail at $T \gtrsim 0.95 T_c$. Using our fits, we also reconstruct the equation of state as a function of real quark and isospin chemical potentials.

hep-lat↗

arXiv2009

Bayesian Inference of Stochastic Volatility Model by Hybrid Monte Carlo

The hybrid Monte Carlo (HMC) algorithm is applied for the Bayesian inference of the stochastic volatility (SV) model. We use the HMC algorithm for the Markov chain Monte Carlo updates of volatility variables of the SV model. First we compute parameters of the SV model by using the artificial financial data and compare the results from the HMC algorithm with those from the Metropolis algorithm. We find that the HMC algorithm decorrelates the volatility variables faster than the Metropolis algorithm. Second we make an empirical study for the time series of the Nikkei 225 stock index by the HMC algorithm. We find the similar correlation behavior for the sampled data to the results from the artificial financial data and obtain a $ϕ$ value close to one ($ϕ\approx 0.977$), which means that the time series has the strong persistency of the volatility shock.

q-fin.CP↗

arXiv2009

Markov Chain Monte Carlo on Asymmetric GARCH Model Using the Adaptive Construction Scheme

We perform Markov chain Monte Carlo simulations for a Bayesian inference of the GJR-GARCH model which is one of asymmetric GARCH models. The adaptive construction scheme is used for the construction of the proposal density in the Metropolis-Hastings algorithm and the parameters of the proposal density are determined adaptively by using the data sampled by the Markov chain Monte Carlo simulation. We study the performance of the scheme with the artificial GJR-GARCH data. We find that the adaptive construction scheme samples GJR-GARCH parameters effectively and conclude that the Metropolis-Hastings algorithm with the adaptive construction scheme is an efficient method to the Bayesian inference of the GJR-GARCH model.

q-fin.CP↗

arXiv2009

Bayesian inference with an adaptive proposal density for GARCH models

We perform the Bayesian inference of a GARCH model by the Metropolis-Hastings algorithm with an adaptive proposal density. The adaptive proposal density is assumed to be the Student's t-distribution and the distribution parameters are evaluated by using the data sampled during the simulation. We apply the method for the QGARCH model which is one of asymmetric GARCH models and make empirical studies for for Nikkei 225, DAX and Hang indexes. We find that autocorrelation times from our method are very small, thus the method is very efficient for generating uncorrelated Monte Carlo data. The results from the QGARCH model show that all the three indexes show the leverage effect, i.e. the volatility is high after negative observations.

q-fin.CP↗

arXiv2009

Bayesian Inference on QGARCH Model Using the Adaptive Construction Scheme

We study the performance of the adaptive construction scheme for a Bayesian inference on the Quadratic GARCH model which introduces the asymmetry in time series dynamics. In the adaptive construction scheme a proposal density in the Metropolis-Hastings algorithm is constructed adaptively by changing the parameters of the density to fit the posterior density. Using artificial QGARCH data we infer the QGARCH parameters by applying the adaptive construction scheme to the Bayesian inference of QGARCH model. We find that the adaptive construction scheme samples QGARCH parameters effectively, i.e. correlations between the sampled data are very small. We conclude that the adaptive construction scheme is an efficient method to the Bayesian estimation of the QGARCH model.

q-fin.CP↗

arXiv2009

An Adaptive Markov Chain Monte Carlo Method for GARCH Model

We propose a method to construct a proposal density for the Metropolis-Hastings algorithm in Markov Chain Monte Carlo (MCMC) simulations of the GARCH model. The proposal density is constructed adaptively by using the data sampled by the MCMC metho d itself. It turns out that autocorrelations between the data generated with our adaptive proposal density are greatly reduced. Thus it is concluded that the adaptive construction method is very efficient and works well for the MCMC simulations of the GARCH model.

q-fin.CP↗

arXiv2008

Financial Time Series Analysis of SV Model by Hybrid Monte Carlo

We apply the hybrid Monte Carlo (HMC) algorithm to the financial time sires analysis of the stochastic volatility (SV) model for the first time. The HMC algorithm is used for the Markov chain Monte Carlo (MCMC) update of volatility variables of the SV model in the Bayesian inference. We compute parameters of the SV model from the artificial financial data and compare the results from the HMC algorithm with those from the Metropolis algorithm. We find that the HMC decorrelates the volatility variables faster than the Metropolis algorithm. We also make an empirical analysis based on the Yen/Dollar exchange rates.

q-fin.ST↗

arXiv2007

Simulations of one-flavor QCD at finite temperature by RHMC

We simulate one-flavor QCD with standard Wilson fermions at finite temperature by the rational hybrid Monte Carlo algorithm. In the heavy quark region when we decrease the quark mass there is an endpoint which terminates the first order phase transition. We try to locate it by calculating the Binder cumulant of the Polyakov loop norm. We estimate the end-point to be kappa_c \sim 0.07-0.08.

hep-lat↗

arXiv2007

Bayesian estimation of GARCH model by hybrid Monte Carlo

The hybrid Monte Carlo (HMC) algorithm is used for Bayesian analysis of the generalized autoregressive conditional heteroscedasticity (GARCH) model. The HMC algorithm is one of Markov chain Monte Carlo (MCMC) algorithms and it updates all parameters at once. We demonstrate that how the HMC reproduces the GARCH parameters correctly. The algorithm is rather general and it can be applied to other models like stochastic volatility models.

physics.comp-ph↗

arXiv2006

Testing and tuning symplectic integrators for Hybrid Monte Carlo algorithm in lattice QCD

We examine a new 2nd order integrator recently found by Omelyan et al. The integration error of the new integrator measured in the root mean square of the energy difference, $\braΔH^2\ket^{1/2}$, is about 10 times smaller than that of the standard 2nd order leapfrog (2LF) integrator. As a result, the step size of the new integrator can be made about three times larger. Taking into account a factor 2 increase in cost, the new integrator is about 50% more efficient than the 2LF integrator. Integrating over positions first, then momenta, is slightly more advantageous than the reverse. Further parameter tuning is possible. We find that the optimal parameter for the new integrator is slightly different from the value obtained by Omelyan et al., and depends on the simulation parameters. This integrator could also be advantageous for the Trotter-Suzuki decomposition in Quantum Monte Carlo.

hep-lat↗

arXiv2005

Simulations of financial markets in a Potts-like model

A three-state model based on the Potts model is proposed to simulate financial markets. The three states are assigned to "buy", "sell" and "inactive" states. The model shows the main stylized facts observed in the financial market: fat-tailed distributions of returns and long time correlations in the absolute returns. At low inactivity rate, the model effectively reduces to the two-state model of Bornholdt and shows similar results to the Bornholdt model. As the inactivity increases, we observe the exponential distributions of returns.

cond-mat.other↗