A stationary time series Xt follows (1 + 0.7B − 0.3B2 )Xt = 0.4 + (1...

A stationary time series Xt follows (1 + 0.7B − 0.3B2 )Xt = 0.4 + (1 + 0.6B4 )Zt. What is the mean of Xt?

Expert Solution

Answer:

(1+0.7B-0.3) Xt= 0.4 + (1+.6) Zt

So, we can write,

Xt +. 7Xt-1- 0.3Xt-2 =0.4+Zt +0.6 Zt-4 [since B js backward operator]

Let mean of the time series is

Taking expectation both side we get

So, E(Xt ) + 0. 7*E(Xt-1) - 0.3E(Xt-2) =0.4+ E(Zt) +0.6* ( Zt-4)

or, + 0.7* - 0.3* =0.4 +0+0 [ Z is white noise so, mean 0]

or,1.4* = 0.4

or, = 0.286

Mean of Xt is 0.286

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orchestra answered 1 year ago

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