Methodology for Time Series Modeling of Demand in e-Commerce

Abstract

This paper proposes a hybrid approach for time series modeling that simultaneously incorporates linear and nonlinear dynamics. Autoregressive (AR) and autoregressive moving average (ARMA) models are applied, with forecasting functions derived from difference equations.

Particular attention is devoted to the identification and treatment of stochastic trends in e-commerce processes. The research investigates the potential origins of such trends, emphasizes the significance of their explicit consideration in forecasting practice, and proposes the application of both the autoregressive integrated moving average (ARIMA) model and the local linear trend (LLT) model. For these specifications, forecasting functions are derived that provide multi-step predictions alongside with conditional expectations.

To address local market fluctuations and consumer sentiment, which typically exhibit nonlinear behavior, the study incorporates radial basis function (RBF) networks. These models enable to describe nonlinear dependencies not only on lagged values of the series but also on exogenous determinants of the process, including product attributes, calendar effects, and other relevant features.

The empirical evaluation is conducted using real sales data obtained from the Amazon platform. Statistical tests are applied to confirm that the data belong to the investigated class of time series. Comparative analysis of the constructed models, based on the forecast accuracy metrics, demonstrates the efficiency of the proposed hybrid methodology. The results indicate that the LLT model provides superior performance in short-term forecasting horizons, whereas ARIMA models are more appropriate for capturing long-term tendencies. The combined approach enhances the adequacy of time series representations and substantially improves the quality of practical forecasting outcomes.