Tax data is a typical time series data, which is subject to the interaction and influence of economic and political factors and has dynamic and highly nonlinear characteristics. The key to correct tax forecasting is the choice of forecasting algorithm. Traditional tax forecasting methods, such as factor scoring method, factor regression method, and system adjustment method, have a certain guiding role in actual work, but there are still many shortcomings, such as the limitation from the distribution and size of sample data and difficulty of grasping the nonlinear phenomena in economic system. Grey-Markov chain model formed by the combination of grey forecasting and Markov chain forecasting can not only reveal the general developmental trend of time series data, but also predict their state change patterns. Based on the summary and analysis of previous research works, this paper expounds the current research status and significance of tax forecasting, elaborates the development background, current status, and future challenges of the Grey-Markov chain model, introduces the basic principles of grey forecasting model and Markov chain model, constructs the Grey-Markov chain model, analyzes the model’s residual error and posteriori error tests, conducts the analysis of Grey-Markov chain model, performs grey forecasting model construction and its state division, implements the calculation of transition probability matrix and the determination of tax forecasting value, discusses the application of the Grey-Markov chain model in tax forecasting, and finally carries out a simulation experiment and its result analysis. The study results show that, compared with separate grey forecasting, Markov chain forecasting, and other commonly used time series forecasting methods, the Grey-Markov chain model increases the accuracy of tax forecasts by an average of 2.3–13.1%. This indicates that the combinative forecasting of Grey-Markov chain model can make full use of the information provided by time series data for tax analysis and forecasting. It can not only avoid the influence of economic, political, and human subjective factors, but also have simple calculations, higher accuracy, and stronger practicality. The study results of this paper provide a reference for further researches on the analysis and application of Grey-Markov chain model in tax forecasting.
