TSFRN: Integrated Time and Spatial-Frequency domain based on Triple-links Residual Network for Sales Forecasting

Sales forecasting plays a critical role in optimizing supply chains, reducing costs, and enhancing customer satisfaction within enterprises. The presence of demand volatility, seasonality, and non-linear relationships with products pose higher requirements for forecasting models. Although deep learning models have demonstrated promising performance in addressing these challenges, the majority of research has primarily focused on modeling historical sales variations and product interactions in the time domain or solely considered periodic representations in the frequency domain within the models. We propose a novel deep learning model TSFRN based on the triple-links residual networks to integrate the time and frequency domain information in this paper, which consists of a forecast link, spatial-frequency forecast link, and a backward link. Specifically, in each block of the network, we first use a recurrent neural network to obtain a time domain prediction of historical sales as the forecast link. Next, we apply the Fast Fourier Transform (FFT) to obtain the frequency domain representation of sales data. Subsequently, a spatial-frequency domain attention mechanism is proposed in this study to capture spatial interaction patterns within the frequency domain of the sales data. Finally, we obtain the prediction based on the frequency domain through an inverse fast Fourier transform as the spatial-frequency forecast link. For the backward link, we minus the forecast link by the input of the current block. Overall, our proposed framework integrates both time domain and frequency domain information to model the complex interrelationships among products. By taking into account both model construction and practical applications, our framework provides a more accurate, effective, and general approach to sales forecasting. Experimental validation on publicly available datasets demonstrates the effectiveness of our proposed model, which outperforms existing methods in predicting product sales with improved accuracy.