In all the following questions, {Z
T E( Z
T k ≠ 0.
) = 0, Var ( Z
T ) = s
Z
2
} is a discrete-time, purely random process, such that and successive values of Z
T are independent so that Cov( Z
1. Show that the ac. f . of the second-order MA process
is given by t = Z
t
+ 0.7Z
ρ( k ) =
1 k = 0
⎪
⎩
⎪
t -1
- 0.2Z
0.37 k = ±1
-0.13 k = ±2
0 otherwise
2. Consider the infinite-order MA process {X
t
}, defined by
X
t
= Z
t
+ C( Z
t -1
+ Z
t -2
t -2
+ !)
where C is a constant. Show that the process is non-stationary. Also show that the series
of first differences {Yt Yt
} defined by
= X
t
- X
t -1
is a first-roder MA process and is stationary. Find the ac. f . of {Y
t
}.
t
, Z
t +k
) = 0,
10 years ago
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