The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Bivariate long range dependent time series forecasting using deep learning

딥러닝을 이용한 이변량 장기종속시계열 예측

  • 김지영 (성균관대학교 통계학과) ;
  • 백창룡 (성균관대학교 통계학과)
  • Received : 2018.11.15
  • Accepted : 2018.12.12
  • Published : 2019.02.28
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Abstract

We consider bivariate long range dependent (LRD) time series forecasting using a deep learning method. A long short-term memory (LSTM) network well-suited to time series data is applied to forecast bivariate time series; in addition, we compare the forecasting performance with bivariate fractional autoregressive integrated moving average (FARIMA) models. Out-of-sample forecasting errors are compared with various performance measures for functional MRI (fMRI) data and daily realized volatility data. The results show a subtle difference in the predicted values of the FIVARMA model and VARFIMA model. LSTM is computationally demanding due to hyper-parameter selection, but is more stable and the forecasting performance is competitively good to that of parametric long range dependent time series models.

본 논문에서는 딥러닝을 이용한 이변량 장기종속시계열(long-range dependent time series) 예측을 고려하였다. 시계열 데이터 예측에 적합한 LSTM(long short-term memory) 네트워크를 이용하여 이변량 장기종속시계열을 예측하고 이를 이변량 FARIMA(fractional ARIMA) 모형인 FIVARMA 모형과 VARFIMA 모형과의 예측 성능을 실증 자료 분석을 통해 비교하였다. 실증 자료로는 기능적 자기공명 영상(fMRI) 및 일일 실현 변동성(daily realized volatility) 자료를 이용하였으며 표본외 예측(out-of sample forecasting) 오차 비교를 통해 예측 성능을 측정하였다. 그 결과, FIVARMA 모형과 VARFIMA 모형의 예측값에는 미묘한 차이가 존재하며, LSTM 네트워크의 경우 초매개변수 선택으로 복잡해 보이지만 계산적으로 더 안정되면서 예측 성능도 모수적 장기종속시계열과 뒤지지 않은 좋은 예측 성능을 보였다.

Keywords

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Figure 3.1. Structure of recurrent neural network.

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Figure 3.2. Example of underfitting, overfitting, and proper fitting.

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Figure 4.1. Example of one step ahead out-of-sample forecasting.

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Figure 4.2. SACF and CCF plot of fMRI data.

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Figure 4.3. Forecasting plot of brain channel 1, 12.

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Figure 4.4. SACF and CCF plot of daily realized volatility data.

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Figure 4.5. Forecasting plot of Nikkei 225, KOSPI.

Table 4.1. Result of fMRI data

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Table 4.2. MASE ratio with FIVAR and LSTM, VARFI and LSTM: fMRI data

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Table 4.3. Result of daily volatility data

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Table 4.4. MASE ratio with FIVAR and LSTM, VARFI and LSTM: Daily volatility data

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Table 4.5. Notation of daily volatility data

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