A comparative study of linear and nonlinear models for aggregate retail sales forecasting

Abstract

The purpose of this paper is to compare the accuracy of various linear and nonlinear models for forecasting aggregate retail sales. Because of the strong seasonal fluctuations observed in the retail sales, several traditional seasonal forecasting methods such as the time series approach and the regression approach with seasonal dummy variables and trigonometric functions are employed. The nonlinear versions of these methods are implemented via neural networks that are generalized nonlinear functional approximators. Issues of seasonal time series modeling such as deseasonalization are also investigated. Using multiple cross-validation samples, we find that the nonlinear models are able to outperform their linear counterparts in out-of-sample forecasting, and prior seasonal adjustment of the data can significantly improve forecasting performance of the neural network model. The overall best model is the neural network built on deseasonalized time series data. While seasonal dummy variables can be useful in developing effective regression models for predicting retail sales, the performance of dummy regression models may not be robust. Furthermore, trigonometric models are not useful in aggregate retail sales forecasting.