본 논문에서는 장기기억 속성을 이용하여 우리나라 주가 변동성을 예측하고 예측성과를 비교한다. 이를 위해 GARCH 모형과 EGARCH 모형에 분수적분 과정을 도입한 FIGARCH 모형과 FIEGARCH모형을 이용하여 표본 외 기간을 예측하고, 이들 모형의 예측성과가 단기기억 변동성 모형(GARCH모형)의 예측성과에 비해 우월한지를 비교한다.
분석 결과 우리나라 주가 변동성에 대해 다음과 같은 사실을 발견하였다. 첫째, 주가에서는 장기기억 속성이 나타나지 않은 것과는 달리 주가 변동성에서는 장기기억 속성이 뚜렷하게 나타났다. 둘째, FIGARCH(1, d, 0) 모형과 FIEGARCH(1, d, 0) 모형의 예측성과가 GARCH(1, 1) 모형의 예측성과에 비해 우월한 것으로 나타났다. 그리고 장기기억 변동성 모형의 상대적 예측성과는 예측기간이 길 때 더 우월한 것으로 나타났다. 본 연구의 결과 장기기억 속성을 이용한 변동성 모형은 예측의 정확도를 높일 수 있는 것으로 나타나, 파생상품의 가격결정이나 VaR 측정 등 위험관리에유용하게 사용될 수 있을 것으로 기대된다.This paper investigates the long-memory property in estimating and
forecasting Korean stock market return volatility. Volatility is a central role
in derivative pricing, portfolio allocation, risk management, and performance
evaluation of funds. In consequence, there has been much research on estimating
and forecasting return volatility. Little has been studied about forecasting
return volatility, however, by exploiting the long-persistent property
in Korean stock market.
In this paper, we estimate and forecast return volatility by employing
the long-memory property. For this purpose, we use the Fractionally Integrated
GARCH and Fractionally Integrated EGARCH models. The estimation
results and forecasting performance of the long-memory volatility models
are compared with those obtained from the short-memory volatility model
such as GARCH model.
Many studies suggest that the conditional volatility of stock returns
follows a long-memory process; shock dissipates at a slow hyperbolic rate.
This type of persistence cannot be appropriately modeled by standard GARCH
type models. In this aspect, the long-memory volatility models are needed
to explain the high-persistent volatility. Baillie et al. (1996) and Bollerslev
and Mikkelsen (1996) suggest the FIGARCH and FIEGARCH models which
introduced the high-persistent property in the standard GARCH and
EGARCH models. Therefore, we used these long-memory volatility models
in forecasting Korean stock market return volatility.
We identified some key findings from the results. First, the auto-
correlations for the absolute and squared returns decline at very slow
rate which suggest that there is a long-memory property in Korean stock
return volatility. Second, it is difficult to say that there is a high-persistent
property in the level of stock returns. However, the return volatility follows
a long-memory process. The estimated values of long-memory parameters,
d of FIGARCH (1, d, 0) and d of FIEGARCH (1, d, 0) models, are 0.356 and
0.584, respectively, and are statistically significant at the 1% significance
level. Third, we conducted out-of-sample one-step-ahead and ten-stepahead
forecasts using the FIGARCH (1, d, 0) and FIEGARCH (1, d, 0) models
and compared the volatility forecasts of both fractionally integrated volatility
models with those of the GARCH (1, 1) model as a benchmark. We found
that the long-memory volatility models produce superior out-of-sample
forecasts in terms of root mean squared error (RMSE), mean absolute error
(MAE), and of Mincer-Zarnowitz regression. In addition, relative forecasting
performance of the ten day ahead forecasts is better than that of
the one day ahead forecasts.
These findings suggest that the long-range volatility models are useful
tools in forecasting the volatility of asset returns as well as pricing derivatives
and hedging risks. The results of this study also will facilitate to induce variance swaps and variance futures in the Korean financial market.