Let us examine the behavior of the variance update in Equation (15.18).

a. Plot the value of a? as a function oft, given various values for a; and 02.

b. Show that the update has a fixed point a2 such that a: a2 as t -+ oo, and calculate the value of 02.

c. Give a qualitative explanation for what happens as a: -+ 0 and as a: --+ 0.