Research and Application of Arima-GBDT Algorithm and Multiple Linear Regression Model

This study focuses on the AHET Dataset, aiming to explore and optimize forecasting methods by combining two predictive models-ARIMA (AutoRegressive Integrated Moving Average) and GBDT (Gradient Boosting Decision Tree)-along with the traditional multiple linear regression model. The ARIMA model excels at capturing trends and seasonal components in time series data, while GBDT can handle non-linear relationships and complex data structures, allowing for a more accurate simulation of actual fluctuations when combined. In specific applications, we first use ARIMA to remove long-term trends and cyclical variations from the raw data, then apply GBDT to fit the residuals, thereby enhancing forecast accuracy. Additionally, we construct a multiple linear regression model as a benchmark for comparison, analyzing the changing trends of different variables. The results show that the hybrid ARIMA-GBDT model performs exceptionally well in forecasting future outcomes, with significantly lower mean squared error compared to single models. This indicates that the combined approach has superior generalization ability and higher predictive accuracy.