Consider the following ARMA(2,1) model yt − yt−1 + 0.1yt−2 = _t − 0.3_t, where _t is white noise (0, _2 _ ). (a) Show that this process is causal and invertible. (b) Calculate the coefficients of the...

Consider the following ARMA(2,1) model

y
t

−


y
t
−1 + 0.1y
t
−2 =
_
t

−

0.3_
t
,

where
_
t
is white noise (0, _2

_
).

(a) Show that this process is causal and invertible.

(b) Calculate the coefficients of the Wold expansion.

(c) Calculate the ACF of
y
t.

Consider the process
{
x
t
}
given

x
t
=
_x
t
−
s
+
z
t
,

with
{
z
t
} _
WN(0, _2),
|
_
|
1 and
s

_
N. Determine the partial autocorrelation

function of
x
t.