H17
HW8 (due Mar. 27).
Exercises 12.4,
12.5 from the textbook and
Problem 1
Consider VARMA model
11
1
tt
t
1
t
−
−
=
Φ+
+
Θ
X
XZ
Z
,
where
1
0.7
0.7
0.7
0.7
⎡
⎤
Φ=
⎢
⎥
⎣
⎦
and
1
0.6
0.4
0.2
0.4
⎡
⎤
Θ=
⎢
⎥
⎣
⎦
.
Is the model stationary and invertible?
Problem 2
Find a statespace representation of the following model:
1
0.6
t
X
ZZ
−
=+
_______________________________________________________________________________________________________
In practice, any sort of signal is usually contaminated by noise.
We’ll assume that the signal is a linear
combination of a set of variables, called
state variables
, which constitute what is called
the
state vector
at time
t
,
t
X
,
describing the state of the system
.
The
statespace model
consists of a
state equation
for the state vector and an
observation equation
.
In its basic form, the equatin for the state vector, the
state equation
, is VAR(1),
1
t
−
t
=
X
XV
,
where
t
X
and
are
v
dimensional,
is a zeromean WN with covariance matrix
Q
,
t
V
t
V
and
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 Spring '09
 gUR
 WT, state vector

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