Takayuki Morimoto

Applications of Double-Wayland Algorithm to Detect Anomalous Signals

The Wayland algorithm has been improved in order to evaluate the degree of visible determinism for dynamics that generate a time series in a simple and accurate manner. Additionally, the Double-Wayland algorithm that we proposed can detect phase transitions among multi-states and non-stationarity in the dynamics. We are applying the Double-Wayland algorithm to detect anomalous signals in railways, stock prices, stabilometry and electrograms recorded by using mapping catheters. In this study, we reported the manner in which these anomalous signals can be detected; however, due to space limitations, we have not reported this data for applications in the field of medicine.

Empirical Comparison of Multivariate GARCH Models for Estimation of Intraday Value at Risk

An empirical comparison of forecasting performance is undertaken for multivariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models in the estimation of intraday value at risk (VaR). This comparison aims to evaluate the applicability of such models to risk management using high-resolution intraday data as a possible method for analyzing intraday downside risk. The one-step-ahead VaR is determined using time-transformed data, and performance of five multivariate models is compared on the basis of the frequency that the estimated VaR exceeds the observed data and a likelihood ratio test of this rate with respect to real returns. It is thus revealed that existing GARCH models can be readily employed for risk management in an intraday framework simply by transforming the high-resolution irregularly spaced data into a regular time series. The Dynamic Conditional Correlation model is found to provide the best forecasting performance among the multivariate GARCH models tested, and this model is thus considered favorable for practical risk management.

Box–Cox realized asymmetric stochastic volatility models with generalized Student's t-error distributions

ABSTRACT This study proposes a class of non-linear realized stochastic volatility (SV) model by applying the Box–Cox (BC) transformation, instead of the logarithmic transformation, to the realized estimator. The non-Gaussian distributions such as Students t, non-central Students t, and generalized hyperbolic skew Students t-distributions are applied to accommodate heavy-tailedness and skewness in returns. The proposed models are fitted to daily returns and realized kernel of six stocks: SP500, FTSE100, Nikkei225, Nasdaq100, DAX, and DJIA using an Markov chain Monte Carlo Bayesian method, in which the Hamiltonian Monte Carlo (HMC) algorithm updates BC parameter and the Riemann manifold HMC algorithm updates latent variables and other parameters that are unable to be sampled directly. Empirical studies provide evidence against both the logarithmic transformation and raw versions of realized SV model.

An Optimal Weight for Realized Variance Based on Intermittent High-Frequency Data

In Japanese stock markets, there are two kinds of breaks, i.e., nighttime and lunch break, where we have no trading, entailing inevitable increase of variance in estimating daily volatility via naive realized variance (RV). In order to perform a much more stabilized estimation, we are concerned here with a modification of the weighting technique of Hansen and Lunde (2005). As an empirical study, we estimate optimal weights in a certain sense for Japanese stock data listed on the Tokyo Stock Exchange. We found that, in most stocks appropriate use of the optimally weighted RV can lead to remarkably smaller estimation variance compared with naive RV, hence substantially to more accurate forecasting of daily volatility.

A Note on a Statistical Hypothesis Testing for Removing Noise by the Random Matrix Theory, and Its Application to Co-Volatility Matrices

It is well known that the bias called market microstructure noise will arise, when estimating realized co-volatility matrix which is calculated as a sum of cross products of intraday high-frequency returns. An existing conventional technique for removing such a market microstructure noise is to perform eigenvalue decomposition of the sum of cross products matrix and to identify the elements corresponding to the decomposed values which are smaller than the maximum eigenvalue of the random matrix as noises. Although the maximum eigenvalue of a random matrix follows asymptotically Tracy-Widom distribution, the existing technique does not take this asymptotic nature into consideration, but only the convergence value is used for it. Therefore, it cannot evaluate quantitatively such a risk that regards accidentally essential volatility as a noise. In this paper, we propose a statistical hypothesis test for removing noise in co-volatility matrix based on the nature in which the maximum eigenvalue of a random matrix follows Tracy-Widom distribution asymptotically.

Robust Estimation of a High-Dimensional Integrated Covariance Matrix

ABSTRACTIn this article, we consider a robust method of estimating a realized covariance matrix calculated as the sum of cross products of intraday high-frequency returns. According to recent artic...

Forecasting Financial Market Volatility Using a Dynamic Topic Model

This study employs big data and text data mining techniques to forecast financial market volatility. We incorporate financial information from online news sources into time series volatility models. We categorize a topic for each news article using time stamps and analyze the chronological evolution of the topic in the set of articles using a dynamic topic model. After calculating a topic score, we develop time series models that incorporate the score to estimate and forecast realized volatility. The results of our empirical analysis suggest that the proposed models can contribute to improving forecasting accuracy.

European Option Pricing Under Fractional Brownian Motion with an Application to Realized Volatility

This study investigates European option pricing under fractional Brownian motion (fBm) and applies it to realized volatility (RV). The RV measure is selected because it uniquely exhibits simultaneous stationarity and long-range dependency properties in financial time series, as shown in our empirical study. Meanwhile, the Black-Scholes differential equation is not well defined when the underlying assets follow fBm with the Hurst exponent H not equal to 1/2 because fBm is not a semimartingale. Thus, we compute the European option prices using a previously proposed fractional Black-Scholes formula. Our empirical study is conducted on Tokyo Stock Price Index data from January 06, 1997 to December 30, 2013 with a sample size of 4177.