is it bad that I have absolutely no recollection of this discussion?
Conditional Expectation of MA(1)
- Thread starter brian.field
- Start date
SyroneDavid
New Member
E[(Yt- theta*(e_t-1))^2| omega_t-1] = E[(e_t)^2 | omega_t-1] = sigma^2
hmm, i need a little bit more clarification from here on, does anyone mind, showing the full steps?
hmm, i need a little bit more clarification from here on, does anyone mind, showing the full steps?
1. Equation
From the definition Yt = e_t + theta * e_t-1
It follows that Yt - theta * e_t -1 = e_t
Plug that into the first expression and you get the second expression
2. Equation
Since e_t is independent of omega_t-1 it follows that also (e_t)^2 is.
That means E[e_t^2 | omega_t-1] = E[e_t^2] = sigma^2
If you have further questions feel free to ask.
From the definition Yt = e_t + theta * e_t-1
It follows that Yt - theta * e_t -1 = e_t
Plug that into the first expression and you get the second expression
2. Equation
Since e_t is independent of omega_t-1 it follows that also (e_t)^2 is.
That means E[e_t^2 | omega_t-1] = E[e_t^2] = sigma^2
If you have further questions feel free to ask.
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