Seasonal differencing from Chapter 11

[aditydev1997]

Statement as per the book official GARP book (chapter 11, seasonal differencing):



How is this equation MA(1)? Isnt this an MA(4) with theta=-1?

And how is this covariance stationary? The characteristic equation is 1+z^4 with complex root of abs value of unity.

 

[David Harper CFA FRM]

Hi @aditydev1997 Yes, I agree and as I recall this mistake has previously observed here in the forum. That should be an MA(4) with θ = {0, 0, 0, 1}. But any MA(q) is stationary. You probably have the wrong characteristic equation. MA(q) is a linear combination of white noise; recall to that an MA(1) translates into AR(∞) so it's not like you can just lag-operate the errors to express MA(q) in terms of lagged observations Y(t-s) values. Thanks,