| Abstract: |
We introduce the performance-based Shapley value (PBSV) to measure the
contributions of individual predictors to the out-of-sample loss for
time-series forecasting models. Our new metric allows a researcher to
anatomize out-of-sample forecasting accuracy, thereby providing valuable
information for interpreting time-series forecasting models. The PBSV is model
agnostic—so it can be applied to any forecasting model, including "black box"
models in machine learning, and it can be used for any loss function. We also
develop the TS-Shapley-VI, a version of the conventional Shapley value that
gauges the importance of predictors for explaining the in-sample predictions
in the entire sequence of fitted models that generates the time series of
out-of-sample forecasts. We then propose the model accordance score to compare
predictor ranks based on the TS-Shapley-VI and PBSV, thereby linking the
predictors' in-sample importance to their contributions to out-of-sample
forecasting accuracy. We illustrate our metrics in an application forecasting
US inflation. |