An Auto Regressive Deep Learning Model for Sales Tax Forecasting from Multiple Short Time Series

This study explores the application of deep learning to forecasting the state of Illinois sale tax receipts in ten categories: general merchandise, food, drinking and eating, apparel, furniture, building and hardware, automotive and filling stations, drugs and retail, agriculture and all others, and manufacturers. The state of Illinois has used traditional techniques of economic and tax receipt forecasting in order to project the amount of resources that it will have in order to finance its activities and debts. Such techniques are mostly linear and lack the ability to model more complex non-linear or long term dependencies. Recently, deep learning models have shown promising results in time series forecasting. In this study, we use two types of neural networks (a simple Multi-Layer Perceptron and a Long Short Term Memory network to forecast the state of Illinois sale tax receipts and compare the performance of both models against the more traditional autoregressive integrated moving Average model. Unfortunately, only limited tax receipt data is publicly made available by the state of Illinois which makes it particularly challenging to train a robust neural network model without overfitting. To address this data limitation, we propose to use a global model with an embedding layer for all ten tax categories. The empirical results show that the global Multi-Layer Perceptron model has the best performance in one step forecasting of Illinois sale tax receipts followed by the global Long Short Term memory model. On average, both neural network models outperformed the traditional Integraded Moving Average model.