This document discusses autoregressive models for financial time series analysis. It introduces autoregressive (AR) and moving average (MA) processes. The autoregressive integrated moving average (ARIMA) model is presented as a way to fit time series data that accounts for correlation between observations. The document outlines the Box-Jenkins methodology for identifying and fitting an ARIMA model to time series data, including checking for stationarity, identifying orders using autocorrelation and partial autocorrelation functions, and selecting the best model. It applies this process to Shanghai Stock Exchange index data, finding that an ARIMA(48,1,0) model provided the best fit.