Supplement to decomposition of mean squared error of weighted geometric mean combined forecasting method

For nonlinear weighted geometric mean combined forecasting method, definitions such as the logarithmic mean square error, logarithmic explanatory power coefficient, and diversity measure are introduced to explore the error decomposition expression on each sub forecasting method from a theoretical perspective, respectively. The logarithmic mean square error of a sub forecasting method is decomposed into three parts: the logarithmic mean error, the logarithmic variance due to the insufficient explanatory power of the model and the logarithmic deviation variance based on the logarithmic explanatory power coefficient. This decomposition provides a reference theory for selecting appropriate sub forecasting methods in the methods pool. By conducting research on local taxation in a certain area, the impact of diversity among sub forecasting methods on mean square error is analyzed through this example.