An empirical investigation of bias and variance in time series forecasting: modeling considerations and error evaluation

Bias and variance play an important role in understanding the fundamental issue of learning and generalization in neural network modeling. Several studies on bias and variance effects have been published in classification and regression related research of neural networks. However, little research has been done in this area for time-series modeling and forecasting. We consider modeling issues related to understanding error components given the common practices associated with neural-network time-series forecasting. We point out the key difference between classification and time-series problems in consideration of the bias-plus-variance decomposition. A Monte Carlo study on the role of bias and variance in neural networks time-series forecasting is conducted. We find that both input lag structure and hidden nodes are important in contributing to the overall forecasting performance. The results also suggest that overspecification of input nodes in neural network modeling does not impact the model bias, but has significant effect on the model variance. Methods such as neural ensembles that focus on reducing the model variance, therefore, can be valuable and effective in time-series forecasting modeling.