Consider the realized volatilities of the Alcoa stock from January 2, 2003, to May 7, 2004, for 340 observations. The realized volatilities are the sum of squares of intraday \(m\)-minute log returns. In this particular instance, we consider three series of realized volatilities obtained, respectively, from 5-minute, 10-minute, and 20-minute intraday \(\log\) returns. The data are in the file aa-3rv.txt. Focus on the \(\log\) series of the realized volatilities.

(a) Identify the Kronecker indices of the three-dimensional log series of realized volatilities.

(b) Use the Kronecker index approach to build a VARMA model for the threedimensional log realized volatilities. Perform model checking and write down the fitted model.

(c) Identify the SCMs for the three-dimensional log series of realized volatilities.

(d) Use the SCM approach to build a VARMA model for the three-dimensional \(\log\) realized volatilities. Perform model checking and write down the fitted model.

(e) Compare and contrast the two VARMA models.