How can I demonstrate that a MA(2) process is invertible?

I have to solve this exercise: Consider the following MA(2) process yt = 1 − 0.5εt−1 + 0.3εt−2 + εt . Is the moving average process invertible? Explain. Hint: Use Matlab to compute the roots of the relevant polynomial. Can anyone help me?.

Thanks

Answer 1

[Pratyush Roy]

Hi,

Since the constant term does not matter in terms of whether the series converges or diverges, we can ignore it and hence the equation can be written as:

Here z(t) = y(t)-1

Now, the relevant polynomial becomes p(x) = 1-0.5x+0.3x^2;

To check whether the model is invertible or not, we compute the roots of p(x) = 0 using the roots method.

Hope this helps!

[Filippo Patrignani]

Thanks