# The Predictive Grey Forecasting Approach for Measuring Tax Collection
## 3 Data and Methodology  
This study considers the data from the financial years of 2000-2001 to 2022-23 for direct and indirect tax collection of India extracted from the Central Board of Directors Tax (CBDT), Government of India ([[https://www.india.gov.in/information-central-board-direct-taxes](https://www.india.gov.in/information-central-board-direct-taxes)]([https://www.india.gov.in/information-central-board-direct-taxes](https://www.india.gov.in/information-central-board-direct-taxes)) accessed on 25 January 2024) and the Ministry of Statistics and Programmed Implementation ([[https://www.mospi.gov.in](https://www.mospi.gov.in)]([https://www.mospi.gov.in](https://www.mospi.gov.in))). Based on the data of 22 years, we forecasted tax collection for 2023-24 to 2029-30 using grey forecasting (GM; 1,1). Grey models and theory have evolved, resulting in a vast literature on theory and applications. The Scopus search engine discovered more than 1,26,000 publications containing \"grey model\" OR \"grey forecasting\" OR \"GM\" from 1854 to 2024 (October). This demonstrates an increased interest in grey models over the last decade. As evident in Appendix A, no previous study has used GM (1,1) for tax forecasting for India; [PERSON] and [PERSON] (2023) found no significant difference in forecasting performance between the fractional grey model (FGM), GM (1,1), and ARIMA (1,1,1). Moreover, [PERSON] and [PERSON] (2024); [PERSON] and [PERSON] (2022) indicated that grey modeling generates more accurate conclusions with limited data points compared to other methodologies and is better suited for forecasting under chaotic and complicated settings with discrete data points. The ability of GM(1,1) to handle limited and uncertain data makes it a good choice for the type of forecasting required in this study. The model suggests that tax collections will continue to grow until the end of this decade due to economic growth and improved tax compliance. While the COVID-19 pandemic posed challenges for accurate predictions, the model still performed reasonably. Compared to more traditional forecasting methods, like ARIMA, grey forecasting offers better accuracy, especially in a complex environment like India's tax system. From a historical perspective, in 1982, [PERSON] introduced grey system theory, designed to perform effectively with a limited number of observations ([PERSON] et al., 2021). The theory is especially useful for systems with incomplete or uncertain information. The purpose of grey system theory is to bridge the gap between the natural and social sciences, allowing it to be used in various fields to solve multiple challenges ([PERSON] et al., 2023). The name \"grey system\" comes from the color representing the subject under analysis. In control theory, the depth of the color indicates how clear the information is ([PERSON] et al., 2021). One well-known concept within this theory is the \"black box\", which is used when the internal features or mathematical formulas describing system dynamics are completely unknown ([PERSON] et al., 2023). The grey forecasting model, or GM (1,1), is a method utilized for predicting limited and short-term datasets, producing an accurate prediction model without requiring the analysis of the statistical distribution of the data involved ([PERSON] et al., 2021). In this framework, \"black\" stands for information that is entirely unknown, \"white\" refers to fully clear and identified information, and \"grey\" represents a mixture of known and unknown details. Therefore, systems with no known information are called black systems, those with fully known details are called white systems, and those with partial knowledge are called grey systems. The term grey system was derived from the color of the subject being examined. In control theory, color depth denotes the degree of information clarity; a prominent variety is called a black box ([PERSON] et al., 2024).