인공신경망 기계학습을 활용한 주가지수 수익률 분석
The Stock Index Return Analysis using the Machine Learning based on Artificial Neural Networks
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초록
주식시장에 대한 기계학습 기반 연구들은 재무이론으로부터 비교적 자유로운 변수들과 최적화 모형을 기반으로 하는 예측의 효율성에 초점이 맞춰진 경향이 있다. 하지만 이러한 기계학습 기반 연구는 주식시장에 대한 기존 재무금융 이론과 상치될 여지가 있다. 따라서, 이 연구는 기존 기계학습 분석에서 소홀히 했던 시계열 데이터들의 임의행보 여부를 검정하는 과정을 거친 후 변수 간의 다중공선성을 고려한 분석 데이터 선정을 통해 재무이론적 관점에 부합하는 연구 기반을 확보하였다. 또한 이들 데이터를 이용한 전통적 회귀분석을 하여 인공신경망 모형들의 기계학습 결과와 비교하기 위한 기반도 마련하였다. 기계학습에는 1, 5, 10 layer MLP 모형과 layer 당 1개의 셀이 있는 1, 5, 10 layer LSTM 모형이 설정되었고, 또한 각 layer 별 활성화 함수 포함 여부에 따라서도 모형을 구분하였다. 학습 결과, 활성화 함수가 포함되지 않은 MLP 모형은 layer의 숫자나 학습 횟수를 늘려도 MSE와 MAE로 측정된 학습 효율성 수준을 개선시키지 못했다. 하지만 학습 과정에 비선형성을 반영할 수 있는 활성화 함수가 포함된 MLP 모형의 학습은 layer의 숫자, 학습 횟수 그리고 입력 데이터 사이즈 증가에 따라서 효율성 개선 효과가 뚜렷이 나타났다. 이에 비해 LSTM 모형에 대한 학습에서는 layer의 숫자, 학습 횟수의 증가가 효율성 개선에 일관된 결과를 제시하지 못하였고, 개선되더라도 영향이 제한적이었다. 다만 입력 데이터 사이즈의 증가는 효율성 개선에 기여한다는 결론을 내릴 수 있었다. LSTM 모형에 대한 이런 결과는 비록 시퀀스 데이터이더라도 KOSPI 수익률과 같이 백색잡음(white noise)이 포함된 시계열 자료에서는 RNN LSTM의 장점이 발휘되기 어렵다는 사실을 보여준다.
Abstract
The Machine learning-based studies on the stock market have tended to focus on the efficiency of prediction based on relatively free variable selection from financial theory and optimization models. Such machine learning-based studies may be at odds with the existing financial theory of the stock market. Therefore, this study secured a research basis that conforms to financial theory by conducting a process of testing the randomness of time series data that was neglected in the machine learning analyses. This analysis, also, selected analysis data which consider multicollinearity among variables. Traditional regression analysis using this data was also conducted to establish a foundation for comparing the machine learning results based on the artificial neural network models. Machine learning involved setting up 1, 5, 10-layer MLP models and 1, 5, 10-layer LSTM models with one cell per layer, and the models were also classified based on whether or not an activation function was included for each layer. The training results showed that the MLP model without activation functions did not improve the efficiency level measured by MSE and MAE, even when the number of layers or training times were increased. However, the training of MLP models that include activation functions, ReLU, which can reflect nonlinearity in the learning process, showed a clear improvement in efficiency with an increase in the number of layers, training times, and input data size. In contrast, in the training of LSTM models, an increase in the number of layers and training times did not consistently show improvement in efficiency, and even when there was improvement, the impact was limited. However, it was concluded that an increase in input data size contributed to improved efficiency. Such results for LSTM models demonstrate that even with sequence data, the advantages of RNN LSTM are difficult to manifest in time series data that include white noise process, such as KOSPI return.
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