00:01
To solve this problem first we have to calculate the auto variance function.
00:06
Auto variance function that is y of h.
00:14
The auto variance function for ma2 process can be calculated using the formula yh is equal to covariance of x t x t minus h.
00:29
Given ma2 process is x underscore t equal to w underscore t plus theta 1 into w t minus 1 plus theta 2 into w underscore t minus 2.
00:49
Next we will calculate the auto covariance for the different lags.
00:55
So for h equal to 0, y of 0 is equal to covariance of x underscore t x underscore t which is equal to expectation of x underscore t.
01:08
Now we will put the required formula of x t in the given formula and after calculation and solving it comes out to be expectation of w underscore t minus 2 square which is equal to 1 and other cross terms are 0.
01:28
Now we will calculate it for h equal to 1.
01:32
So that is we are going to calculate the y of 1.
01:38
So it is equal to covariance of x t x t minus 1 which after calculation come out to be theta 1 plus theta 1 theta 2.
01:49
Next now we will calculate it for h equal to.
01:53
So y of 2 equal to covariance of x underscore t x underscore t minus 2 which comes out to be theta 2 and for all other value of h y of h is equal to 0...