Having established how to decompose time series, test for stationarity, and identify potential model structures using ACF and PACF plots in the previous chapters, we now focus on building statistical forecasting models. This chapter introduces the Autoregressive Integrated Moving Average (ARIMA) family of models, a widely used class for analyzing and predicting stationary time series data.

You will learn about the core building blocks:

• Autoregressive (AR) models: How past values influence the current value.
• Moving Average (MA) models: How past forecast errors influence the current value.
• ARMA models: Combining AR and MA components for stationary series.
• ARIMA models: Incorporating differencing (the 'Integrated' part) to handle non-stationary series before applying ARMA modeling.

We will cover the process of specifying the ARIMA model order, denoted as ($p, d, q$), using insights gained from ACF/PACF analysis. You'll see how to fit these models to data using Python's statsmodels library, diagnose the model's fit by examining residuals, and generate forecasts for future time points. The chapter concludes with hands-on practice in building and evaluating a complete ARIMA forecasting workflow.