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I am struggling with a math problem set question and just wanting some pointers:

I have this a stationary time series (MA(h)) that satisfies this equation below and has the sigma^2 below

xt=(ut+ut-1+ut-2+...ut-m)/m+1 with Var(x)=4.0

how do I figure out the roh(h) the auto correlation function of this?

-it is given as (m+1-h)/m+1 <= h <=1 but I don't know how to get to that point

-I do know:

--sigma(h)/sigma(0) = ACF (sigma =autocovariance of 0 and h)

--sigma(h) = variance [sum aplha(i)*alpha(i+h)] if i<=q 0 else wherd

--when h =0 acf(h)=1 to start then it degrades to 0

any hints on where to start here?

R.Merritt
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  • ACF(s, t) = E[x(s) x(t)], right? Why not plug definition of x into that expression and see what you get? Without looking into details, I'm going to guess that ACF(s, t) = 0 when abs(s - t) > m and some nonzero value otherwise. Also, maybe stats.stackexchange.com is a better forum for a question of this kind. – Robert Dodier Jan 21 '16 at 21:05
  • hmmm still not sure how to plug my definition in there – R.Merritt Jan 22 '16 at 02:04
  • Wouldn't you want to write `E[x(s) x(t)] = E[(u(s) + ... + u(s - m)) (u(t) + ... + u(t - m))]/(m + 1)^2` and go from there? I think you'll get a lot of terms like `E[u(s - j) u(t - k)]` which is 0 if `s - j != t - k` and some constant otherwise. – Robert Dodier Jan 22 '16 at 02:49
  • ok cool thats great info thanks Robert! – R.Merritt Jan 22 '16 at 05:17

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