A comparison of vector SHAP explanations of the S&P 500 realized volatility forecast by LSTM and ADL models

Analyzing the contribution of each predictor variable in forecasting models is a critical task.To address this, Lundberg and Lee (2017) proposed the SHAP (SHapley Additive exPlanations) as a method to explain the contribution of individual predictors in machine learning forecasts.However, in time series forecastings that require consideration of lagged variables, the SHAP requires heavy computation and makes it difficult to evaluate the contribution of predictor vectors composed of lagged variables.To overcome these limitations, Choi et al. (2024) introduced the vector SHAP, which measures the contribution of each predictor vector composed of variable lags.The vector SHAP not only reduces computation compared to the SHAP but also provides insights into the contributions of predictors that include lagged variables.In this study, we construct realized volatility forecasting models for the S&P 500 using realized volatility, implied volatility, the search volume index, and their lagged variables as predictors, and apply the vector SHAP to evaluate their contributions.We compare the predictor vector contributions in two models: the ADL model, a statistical time series framework, and the LSTM model, a machine learning approach.The results show that past realized volatility has the most significant impact on forecasting realized volatility, while the search volume index contributes only marginally.In the ADL model, multicollinearity often obscures the interpretation of predictor contributions, whereas this limitation is considerably reduced in the LSTM model.Furthermore, unlike in the ADL model, the LSTM model reveals nonlinear contributions of the search volume index.