Measuring Business Cycle Turning Points in Japan with a Dynamic Markov Switching Factor Model

In the dynamic factor model, a single unobserved factor common to some macroeconomic variables is defined as a composite index to measure business cycles. This model has recently been developed by combining with the regime switching model so that the mean growth of the index may shift depending on whether the economy is in a boom regime or in a recession regime. An advantage of this dynamic Markov switching factor model is that estimating the model by a Bayesian method produces the posterior probabilities that the economy is in the recession regime, which can be used to date the business cycle turning points. This article estimates the dynamic Markov switching factor model using some macroeconomic variables in Japan. The model comparison using the Bayes factor does not provide strong evidence that the mean growth of the index shifts, but the dynamic Markov switching factor model is found to produce the estimates of turning points close to the reference dates of the Economic and Social Research Institute in the Cabinet Office, unless only weakly correlated variables are used.

Bayesian Analysis of Time-Varying Parameter Vector Autoregressive Model with the Ordering of Variables for the Japanese Economy and Monetary Policy

This paper applies the time-varying parameter vector autoregressive model to the Japanese economy. The both parameters and volatilities, which are assumed to follow a random-walk process, are estimated using a Bayesian method with MCMC. The recursive structure is assumed for identification and the reversible jump MCMC is used for the ordering of variables. The empirical result reveals the time-varying structure of the Japanese economy and monetary policy during the period from 1981 to 2008 and provides evidence that the order of variables may change by the introduction of zero interest rate policy.Bayesian inference, Monetary policy, Reversible jump Markov chain Monte Carlo, Stochastic volatility, Time-varying parameter VAR

"Block Sampler and Posterior Mode Estimation for Asymmetric Stochastic Volatility Models"

This article introduces a new efficient simulation smoother and disturbance smoother for asymmetric stochastic volatility models where there exists a correlation between today's return and tomorrow's volatility. The state vector is divided into several blocks where each block consists of many state variables. For each block, corresponding disturbances are sampled simultaneously from their conditional posterior distribution. The algorithm is based on the multivariate normal approximation of the conditional posterior density and exploits a conventional simulation smoother for a linear and Gaussian state space model. The performance of our method is illustrated using two examples (1) simple asymmetric stochastic volatility model and (2) asymmetric stochastic volatility model with state-dependent variances. The popular single move sampler which samples a state variable at a time is also conducted for comparison in the first example. It is shown that our proposed sampler produces considerable.

Block Sampler and Posterior Mode Estimation for Asymmetric Stochastic Volatility Models (Published in "Computational Statistics and Data Analysis", 52-6, 2892-2910. February 2008. )

This article introduces a new efficient simulation smoother and disturbance smoother for asymmetric stochastic volatility models where there exists a correlation between today`s return and tomorrow`s volatility. The state vector is divided into several blocks where each block consists of many state variables. For each block, corresponding disturbances are sampled simultaneously from their conditional posterior distribution. The algorithm is based on the multivariate normal approximation of the conditional posterior density and exploits a conventional simulation smoother for a linear and Gaussian state space model. The performance of our method is illustrated using two examples (1) simple asymmetric stochastic volatility model and (2) asymmetric stochastic volatility model with state-dependent variances. The popular single move sampler which samples a state variable at a time is also conducted for comparison in the first example. It is shown that our proposed sampler produces considerable improvement in the mixing property of the Markov chain Monte Carlo chain.

"Modeling and Forecasting the Volatility of the Nikkei 225 Realized Volatility Using the ARFIMA-GARCH Model"

In this paper, we apply the ARFIMA-GARCH model to the realized volatility and the continuous sample path variations constructed from high-frequency Nikkei 225 data. While the homoskedastic ARFIMA model performs excellently in predicting the Nikkei 225 realized volatility time series and their square-root and log transformations, the residuals of the model suggest presence of strong conditional heteroskedasticity similar to the finding of Corsi et al. (2007) for the realized S&P 500 futures volatility. An ARFIMA model augmented by a GARCH(1,1) specification for the error term largely captures this and substantially improves the fit to the data. In a multi-day forecasting setting, we also find some evidence of predictable time variation in the volatility of the Nikkei 225 volatility captured by the ARFIMA-GARCH model.

A State Space Approach to Estimating the Integrated Variance and Microstructure Noise Component

We call the realized variance (RV) calculated with observed prices contaminated by microstructure noises (MNs) the noise-contaminated RV (NCRV) and refer to the component in the NCRV associated with the MNs as the MN component. This paper develops a method for estimating the integrated variance (IV) and MN component simultaneously, extending the state space method proposed by Barndorff-Nielsen and Shephard (2002). Our extension is based on the result obtained in Meddahi (2003), namely, when the true log-price process follows a general class of continuous-time stochastic volatility (SV) models, the IV follows an ARMA process. We represent the NCRV by a state space form and show that the state space form parameters are not identifiable; however, they can be expressed as functions of fewer identifiable parameters. We illustrate how to estimate these parameters. The proposed method is applied to yen/dollar exchange rate data. We find that the magnitude of the MN component is, on average, about 21%-48 % of the NCRV, depending on the sampling frequency.Realized Variance, Integrated Variance, Microstructure Noise

Modeling and Forecasting the Volatility of the Nikkei 225 Realized Volatility Using the ARFIMA-GARCH Model

In this paper, we apply the ARFIMA-GARCH model to the realized volatility and the continuous sample path variations constructed from high-frequency Nikkei 225 data. While the homoskedastic ARFIMA model performs excellently in predicting the Nikkei 225 realized volatility time series and their square-root and log transformations, the residuals of the model suggest presence of strong conditional heteroskedasticity similar to the finding of Corsi et al. (2007) for the realized S&P 500 futures volatility. An ARFIMA model augmented by a GARCH(1,1) specifi-cation for the error term largely captures this and substantially improves the fit to the data. In a multi-day forecasting setting, we also find some evidence of predictable time variation in the volatility of the Nikkei 225 volatility captured by the ARFIMA-GARCH model.

Block Sampler and Posterior Mode Estimation for A Nonlinear and Non-Gaussian State-Space Model with Correlated Errors

This article introduces a new efficient simulation smoother and disturbance smoother for general state-space models where there exists a correlation between error terms of the measurement and state equations. The state vector is divided into several blocks where each block consists of many state variables. For each block, corresponding disturbances are sampled simultaneously from their conditional posterior distribution. The algorithm is based on the multivariate normal approximation of the conditional posterior density and exploits a conventional simulation smoother for a linear and Gaussian state space model. The performance of our method is illustrated using two examples (1) stochastic volatility models with leverage effects and (2) stochastic volatility models with leverage effects and state-dependent variances. The popular single move sampler which samples a state variable at a time is also conducted for comparison in the first example. It is shown that our proposed sampler produces considerable improvement in the mixing property of the Markov chain Monte Carlo chain.