Korean Stock Price Index Volatility and Japanese Stock Price Index Volatility
Authors:   Asia-Europe Perspective Association, Yoo Han-Soo 
Published: June 2018

In this paper, I investigate empirically lead-lag relationship between KOSPI200 volatility and NIKKEI225 volatility. There is a strong economic relationship between Korea and Japan in investment and international trade. Previous studies have been concentrated on the first moment of stock price index and observed volatility. In research angle, the analysis in this study is distinguished from previous studies in that this paper is concentrated on permanent volatility and transitory volatility. That is, the contribution of this paper is investigating the relationship between KOSPI200 permanent volatility and NIKKEI225 permanent volatility and the relationship between KOSPI200 transitory volatility and NIKKEI225 transitory volatility. Permanent volatility means the long-run component of observed volatility and transitory volatility means the short-run component of observed volatility. Observed volatility, permanent volatility and transitory volatility are estimated by using Component GARCH model. In Component GARCH model, observed volatility is assumed as the sum of permanent component and transitory component. Permanent volatility component has nearly a unit root, and transitory volatility component has a rapid time decay. That is, the long-run component is more persistent and mean-reverts much slower than short-run component.
The sample period in this paper ranges from 4 January 2005 to 30 October 2009. Because Korean stock market holidays differ from Japanese stock market holidays, the corresponding date in another country which is a holiday in one country is deleted in the data set.
I check the statistical features of the data. The summary statistics of stock price index return are as follows. KOSPI200 and NIKKEI225 time series data have the features of stock return as spiked peak and persistence. Ex ante ARCH LM tests show that there are ARCH effects in the residuals. Therefore, GARCH type is appropriate for these series.
The procedure used in this paper involves the following steps. First, to estimate observed volatility, permanent volatility and transitory volatility, this study employs Component GARCH model. In Component GARCH model, variance equation is expressed as follows: [수식]. That is, observed volatility is assumed as the sum of permanent volatility component and transitory volatility component. The Component GARCH model estimation results show that AR coefficients of long-run component of KOSPI200 and NIKKEI225, ρ, are nearly one, and persistent rates of short-run component, α1+β1, are smaller than ρ.
In the second step, before examining the lead-lag relations, the unit root test to check the stationarity of each series is first employed. To test for the existence of a unit root, Augmented Dickey-Fuller test is used. The appropriate lag length is determined by the Schwartz Criterion. In each case of volatilities, ADF test results show that the null hypothesis that the series has a unit root is rejected. That is, observed volatility, permanent volatility and transitory volatility are stationary series. Therefore, level series is used in VAR model for Granger causality test in this study.
In the third step, to examine the lead-lag relationship between KOSPI200 volatility and NIKKEI225 volatility, Granger causality tests are performed. Granger causality test is a useful tool to uncover the direction of causality. Granger causality test examines whether the past values of a variable, NIKKEI225 volatility, helps explain the current value of another variable, KOSPI200 volatility. Observed volatility, permanent volatility and transitory volatility data are found to be stationary series. Therefore, Granger causality test based on VAR is applied. The Granger causality tests show that there are bidirectional Granger causalities between KOSPI200 observed volatility and NIKKEI225 observed volatility.