H8
HW4 (due Feb. 7).
Exercises 5.1, 5.2 from the textbook and
Problem 1
Suppose that in a sample of size 100, you obtain
ˆ(1)
0.432
ρ
=
and
ˆ(2)
0.145
=
.
Assuming that the data were generated from an MA(1) model, construct approximate 95%
CIs for
(1)
and
(2)
.
Based on these two confidence intervals, are the data consistent
with a MA(1) model with
0.6
θ
=
?
Problem 2
The graphs below show the sample ASF (left) and PASF (right) of a time series.
On the basis
of the available information, choose an ARMA model for the data and explain your choice.
1.00
.80
.60
.40
.20
.00
.20
.40
.60
.80
1.00
0
5
10
15
20
25
30
35
40
Sample ACF
0
5
Sample PACF
_______________________________________________________________________________________________________
The
prediction problem
: from the observed values of a time series at
past
points,
1
, ... ,
t
X
X
,
predict the value it will assume at some specific
future
time point,
+
th
X
.
In forecasting
X
+
,
t
is called the
forecast origin
and positive integer
h
is the
forecast horizon
.
We refer to
as the
h
step ahead forecast of
ˆ
X
+
t
X
at the forecast origin
.
t
The accuracy of
is measured in terms of the
smallness
of the quantity
ˆ
+
X
( )
2
ˆ
EX
X
++
−
.
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 Spring '09
 gUR
 Forecasting, Normal Distribution, Probability theory, Conditional expectation, zt

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