Ec 178 RECENT EXAMS
Midterm  Winter 2006
Problem 1
You have data y
t
, t = 1…6, in Table
A.
A.
Compute simple moving
average (m = 2), EWMA (α =
0.4), CMA (m = 3), and 1
st
differences.
B.
Use SES (α = 0.4) to compute
forecast ŷ
7
.
Problem 2
Lake level data y
t
, t = 1…13, are
shown in Table B.
The series was
smoothed and forecasted by Holt’s
TwoParameter DES with α = 0.6 and
β = 0.2.
A.
Fill in the unshaded blank cells in
the table, including
ex ante
fore
casts ŷ
14
and ŷ
15
.
B. Explain how you could compute an
approximately 95% prediction
interval forecast for any future time
period n+h.
Problem 3
Fig. 1 shows a firm called “Victim.”
They introduced a new product and
sales grew well until an outside party
allegedly injured the company, giving
rise to a “business interruption”
lawsuit.
Your consulting team
is to forecast what sales
would
have been
if the interruption
had NOT occurred.
You have
the following data:
•
y
t
= sales, t = 1…37
•
lny
t
= Ln(y
t
)
Table A  Filters
t
y
t
yˉ
(2)
t
(0.4)
t
CMA(3)
t
(1L)y
t
1
107
2
126
3
132
4
106
5
118
6
105
7
< 
Forecast
Table B – Lake Level
t
y
t
S
t
D
t
ŷ
t1,1
1
31
2
28
28.000
3.000
3
28
26.800
2.640
4
27
25.864
2.299
5
26
25.026
2.007
6
25
24.208
1.769
23.019
7
16
18.575
2.542
22.438
8
18
17.213
2.306
16.033
9
18
16.763
1.935
14.908
1
0
12
13.131
2.274
14.828
1
1
11
1
2
7
7.674
2.459
8.686
1
3
5
5.086
2.485
5.215
1
4
<  Ex ante forecasts
1
5
Fig. 1  Victim Sales ($1000/month)
$0
$100
$200
$300
$400
$500
$600
$700
$800
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37
y
yfit
yf'cast
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Recent Exams
p. 2
•
d
t
= interruption dummy variable, d = 0 before the interruption (t = 1…20) and d = 1 after the
interruption began (t = 21…37)
You ran the following regression in S
TATA
over period t = 1…37:
nl (lny = {b0} + {b1}*d + {b2}/t + {b3}*d/t)
The regression results are in Table C.
In Fig. 1, fitted values
from this regression are shown as “yfit” and your forecast of
sales
if no interruption had occurred
are “yf’cast.”
A. What is the name of the curve you used to represent
Victim’s uninterrupted sales pattern?
B.
If the interruption had not occurred, your model predicts
that Victim sales would eventually reach what level?
C. Compute the forecasted (uninterrupted) value of sales for period t = 30.
ŷ
30
= __________
Problem 4
A school has three 4month trimesters each year.
Let y
t
= number of students enrolled/trimester.
Table D shows the results of three regressions based on the seasonal dummy variable model:
•
y
t
= β
1
+ β
2
A(2)
t
+ β
3
A(3)
t
+ β
4
t + β
5
t
2
+ u
t
, t = 1 …15.
Table D
Estimated Coefficient (tstats in
parentheses)
Regression
β
1
β
2
β
3
β
4
β
5
R
2
#1
32.7
(4.40)
5.24
(2.46)
0.335
(2.59)
0.360252
#2
50.6
(13.4)
11.5
(2.15)
0.343
(0.06)
0.346762
#3
36.0
(6.48)
11.7
(3.09)
0.621
(0.16)
5.38
(3.53)
0.345
(3.74)
0.728076
A. Test for seasonality at the α = 5% level of statistical significance.
•
H
0
:
_______________
H
1
:
_______________
•
Test statistic = __________
•
5% critical value(s) = _________________
•
{ Accept
Reject } H
0
and conclude that there { is
is not } seasonality in the data.
B. Assuming there IS seasonality, compute
ex ante
forecast for periods t = 16 (1
st
trimester) and
t = 17 (2
nd
trimester).
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