Vector SHAP Values for Machine Learning Time Series Forecasting

We propose a new vector SHapley Additive exPlanations (SHAP) to interpret machine learning models for forecasting time series using lags of predictor variables. Unlike the standard SHAP measuring the contribution of each lag of each predictor variable, the proposed vector SHAP measures the contribution of the vector of the lags of each variable. The vector SHAP has an advantage of faster computation over the standard SHAP. Some desirable properties of the vector SHAP (vector local accuracy, vector missingness, and vector consistency) are established. A Monte Carlo simulation shows that the vector SHAP has a much faster computing time than the SHAP; the difference of the standard SHAP and the vector SHAP is small; the sampling SHAP is sensitive to the sampling proportion in a range of practical application; the vector SHAP mitigates the sensitivity issue. The vector SHAP is applied to the realized volatility of world major stock price indices of 16 countries for forecasting the realized volatility of South Korea stock price index, KOSPI. Further vectoring by regions of Europe, North America, and Asia yields vector SHAP value for each region which is very close to the sum of vector SHAP values of the countries of the region, illustrating usefulness of the strategy of vectoring.