Implementation of Autoregressive Integrated Moving Average (ARIMA) Model

In the MATLAB environment, we have successfully implemented the Autoregressive Integrated Moving Average (ARIMA) model. This model represents a sophisticated time series forecasting methodology capable of predicting future trends. During implementation, we extensively utilized MATLAB's specialized tools and functions, including time series objects handling through `timetable` data structures and ARIMA modeling functions such as `arima()` for model specification and `estimate()` for parameter optimization. The implementation process involved systematic data analysis procedures, including historical data collection and preprocessing using functions like `readtable()` and `data preprocessing` techniques. We employed stepwise parameter optimization through maximum likelihood estimation (MLE) methods, utilizing MATLAB's optimization algorithms to enhance model accuracy and stability. The experimental results demonstrate satisfactory performance, providing valuable reference framework for future research in time series forecasting. Key implementation aspects included differencing operations using `diff()` function for stationarity achievement, autocorrelation analysis via `autocorr()` function, and model validation through residual analysis with `infer()` function for forecast error examination.