(a.)Download the DJIA data from Yahoo! Finance using quantmod (the index ticker is ^DJI) from 1991-01-01 to 2019-06-30 and calculate the daily return time series.

(b.) Write down the AR model for the series. Remove insignificant coefficient estimates (based

on t-ratio in absolute value of 1.645). Provide model checking to confirm that the model is adequate.

(c.) Use the fitted model to obtain 1-step to 4-step ahead predictions series (forecast origin is the last data point). Also, compute the corresponding 95% interval forecasts.

(d.). Does the series exhibit GARCH effects? If yes, why?

(e.) Provide the volatility equation and perform model checking. Consider both a normal innovation and a Student-t innovation.

(f.) Write the full model for the series.