This study proposes a class of realized non-linear stochastic volatility models with asymmetric effects and generalized Student's t-error distributions by applying three families of power transformation-exponential, modulus, and Yeo-Johnson-to lagged log volatility. The proposed class encompasses a raw version of the realized stochastic volatility model. In the Markov chain Monte Carlo algorithm, an efficient Hamiltonian Monte Carlo (HMC) method is developed to update the latent log volatility and transformation parameter, whereas the other parameters that could not be sampled directly are updated by an efficient Riemann manifold HMC method. Empirical studies on daily returns and four realized volatility estimators of the Tokyo Stock Price Index (TOPIX) over 4-year and 8-year periods demonstrate statistical evidence supporting the incorporation of skew distribution into the error density in the returns and the use of power transformations of lagged log volatility.
Volatiliy measurement and modeling is an important aspect in many areas of finance. The main purpose of this study is to apply seven APARCH-type models with (1,1) lags to investigate the behavior of exchange rate volatility for the EUR, JPY, and USD selling exchange rates to IDR for the duration from January 2010 to December 2015. The competing models include ARCH, GARCH, TARCH, TS-ARCH, GJR-GARCH, NARCH, and APARCH used with Gaussian normal distribution. In order to estimate the model parameters, this study applies the Bayesian inference using the adaptive random walk Metropolis method in the MCMC algorithm. Empirical results based on the deviance information criterion indicate that the GARCH (1,1), APARCH (1,1), and TARCH (1,1) models provide the best fit for the EUR, JPY, and USD data, respectively. In those models, both the JPY and USD data have significant negative leverage effect at the 99% credible level. Moreover, the JPY returns also have significant Taylor effect in return volatility at the 99% credible level.
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