마코프전환 멀티프랙탈(Markov Switching Multifractal) 모형을 이용한 KOSPI200 수익률의 장기변동성 예측성과 비교

국문 초록 (Abstract)

금융시계열 변동성에 관하여 잘 알려진 특징은 변동성군집현상, 장기기억성, 국면전환, 그리고 특이치의 존재 등이다. 작은 수의 파라미터를 사용함에도 불구하고 이러한 특징들을 동시에 잘설명하는 것으로 알려진 마코프전환 멀티프랙탈(Markov Switching Multifractal: MSM) 변동성모형을 이용하여 우리나라 KOSPI200 지수의 변동성을 추정하고 다기간 예측성과를 비교 분석하였다. 표본기간은 2003년 1월 2일부터 2014년 12월 30일까지이며 비교 모형으로는 벤치마크모형으로 많이 사용되고 있는 GARCH 모형과 국면전환 GARCH 모형을 사용하였다. 실증분석 결과 내표본 모형 적합도와 사후표본 예측성과 측면에서 모두 MSM 모형이 비교대상 모형에 비해 전반적인 우위를 보였으며 익일변동성 예측뿐만 아니라 주간 및 월간으로 예측 기간을 증가시킬수록 이러한 경향이 더욱 강한 것으로 나타났다. MSM 모형의 부산물로 KOSPI200 지수 수익률의 변동성을 각각의 변동성 요소의 듀레이션의 크기에 따라 단기 및 중·장기 변동성 부분으로 분해할 수 있는데 2008년 글로벌 금융위기와 2011년 유럽 재정위기 기간의 경우 변동성의 속성이 크게 다르다는 것을 확인하였다. 글로벌 금융위기의 경우 단기 및 중기빈도의 변동성뿐만 아니라 저빈도의 장기변동성 또한 높아져 한국주식시장을 높은 변동성 국면으로 전환시켰던 것으로 나타났지만 유럽 재정위기 기간에서는 단기와 중기빈도 변동성은 높아진 반면 저빈도의 변동성 국면전환은 발생하지 않아 한국 주식시장에 대한 영향은 비록 컸으나 상대적으로 일시적이었던 것으로 나타났다.

다국어 초록 (Multilingual Abstract)

Volatility clustering, long memory, regime change, and the presence of outliers are wellknown stylized facts of volatility of financial time series. This paper estimates the volatility model of KOSPI200 index returns using a Markov switching multifractal (MSM) model that is known to capture these characteristics with relatively small number of parameters and compares its multi-horizon forecasting performance with that of popular competing models such as a standard GARCH model and Markov switching GARCH model. Using the sample period covering from January 2, 2003 to December 30, 2014, this paper finds that the MSM model outperforms competing models in terms of both in-sample goodness of fit and out-of-sample forecasting performance. Particularly, the forecasting performance tends to become more prominent as the forecasting horizon increases. As a byproduct the MSM model allows KOSPI200 return volatility to be decomposed into short-term and medium- to long-term volatility components. The examination of computed volatility components suggests that the nature and effect of volatilities due to the 2008 global financial crisis and 2011 European sovereign debt crisis are quite different: in addition to the increase in short- and medium-term volatilities, the low-frequency longterm volatility is also increased during the former crisis period resulting in Korean stock market shifting into the higher volatility state, whereas the shift in the volatility state is not observed during the latter crisis period implying that the effect of European debt crisis to Korean stock market was big, but only transitory.

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