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고빈도 수익률과 실현변동성을 이용한 금융자료의 통계적 속성에 관한 재고찰

  • 엄철준 부산대학교 경영대학 교수
본 연구는 한국 주식시장의 KOSPI 200 시장지수와 국제외환시장의 일본 엔(USD/JPY) 환율의 일중 고빈도 자료를 이용하여 다양한 수익률 측정시간 간격으로부터 산출된 수익률과 실현변동성에 대한 분포적 및 동적 속성을 실증적으로 조사하였다. 주요 검증결과에 의하면, KOSPI 200 시장지수와 일본 엔 환율의 수익률 실증적 분포에 대한 통계적 속성은 정규분포와 분명한 차이를 갖고, 수익률 측정시간 간격의 차이는 분포의 정규성 정도에 의미 있는 영향을 미쳤다. 또한 재무 분야에서 널리 알려진 수익률 분포의 높은 중심부분과 두꺼운 꼬리부분의 특징은 신뢰구간 90% 수준과 유의수준 0.5% 수준에서 각각 확인되는 현상임을 발견하였다. 다음으로, 고빈도 수익률자료로부터 산출된 실현 분산과 실현표준편차는 로그정규분포에 유사한 특징을 보였지만, 로그변환 실현표준 편차는 정규분포의 속성에 가까웠다. 그리고 수익률을 실현표준편차로 표준화한 조정된 수익률은 일반적으로 잘 알려진 수익률과 달리 정규분포에 매우 근접한 특징을 보였다. 이상에서 언급한 수익률과 실현변동성의 통계적 속성은 주식시장과 외환시장에 관계없이 관찰되는 공통성을 가졌다.
실현변동성; 고빈도 자료; 수익률 측정시간 간격; 분포적 속성; 동적 속성; Realized Volatility; High-Frequency Data; Time Scale Effect; Distributional Property; Dynamic Property

A Re-Examination of the Statistical Characteristics of Financial Time Series using Intraday High-Frequency Returns and Realized Volatility

  • Cheoljun Eom
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.