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Asian Review of Financial Research Vol.28 No.3 pp.453-485
A Re-Examination of the Statistical Characteristics of Financial Time Series using Intraday High-Frequency Returns and Realized Volatility
Cheoljun Eom* Professor, School of Business, Pusan National University
Key Words : Realized Volatility,High-Frequency Data,Time Scale Effect,Distributional Property,Dynamic Property


This study used intraday high-frequency data over a 10-year period to empirically investigate the distributional and dynamic properties of returns and measurements of realized volatility in a situation of high market liquidity in the KOSPI 200 stock market index and the Japanese yen foreign exchange rate. The purpose and scope of the research were as follows. First, we examined the statistical characteristics of the empirical distribution of each return using high-frequency price data with eight time scales ranging from 1 min to 1 day, and determined the degree of difference from a normal distribution and the effect of increasing the measurement time interval from 1 min to 1 day. Second, we investigated the distributional and dynamic properties of the empirical distribution of each measurement of realized volatility calculated from the high-frequency returns, and the distribution of adjusted returns divided by the realized volatility. The empirical distribution of the returns from the KOSPI 200 market index and the Japanese yen exchange rate clearly differed from a normal distribution, with a more peaked central part and a much fatter tail. The time scale used to calculate the returns had a significant influence on the results; the shorter the measurement time scale, the larger the deviation from a normal distribution. Additionally, we found that the higher central part and much fatter tail of the empirical distribution of the returns, compared with a normal distribution, was supported at the 90% confidence interval in the central part and a significance level of 0.5% of the confidence interval in the tail. [The description of the confidence intervals and significance levels with respect to the center and tail of the distribution needs to be clarified.] The dynamic properties of the returns did not persist over time, decaying slowly according to changes in the autocorrelation from lag 1 to lag 100; that is, the distribution displayed unpredictability. The realized variance and realized standard deviation of volatility calculated from the highfrequency KOSPI 200 market index data and the Japanese yen exchange rate had the characteristics of a log-normal distribution, with a higher central part and a tail that was highly skewed to the right, whereas the distribution of the logarithmic realized standard deviation was similar to a normal distribution. The predictability of the measurements of the realized volatility was confirmed by time series persistence, in which the autocorrelation of the realized volatility decreased slowly according to the change from lag 1 to lag 100. Interestingly, the adjusted return divided by the realized standard deviation showed very similar characteristics to a normal distribution, unlike the distributional properties of the original return. Based on the observed distributional and dynamic properties of the returns and the realized volatility, commonality may exist regardless of the type of market. These findings suggest that there is a need to carefully consider the distribution and dynamic properties of returns when establishing an empirical design using intraday high-frequency data. An increasing number of studies have reported results based on empirical designs using intraday high-frequency data, and researchers have tried to control for the negative effects of market liquidity, measurement errors, and market microstructure. Unfortunately, however, they have not seriously considered the possibility that the time scale used to calculate the returns might influence the results. The main findings of this study suggest that time scales may be crucial influencing factors when establishing the design of an empirical test.
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