FIN7028
Exam Time Table Code FIN7028
EXAMINATION FOR THE DEGREE OF
MASTER OF SCIENCE (FINANCE) AND OTHER DEGREES
TIME-SERIES FINANCIAL ECONOMETRICS
Monday, 29th May 2017 9:30 AM - 11:30 AM
Examiners: Professor Gerhard Kling
and the internal examiners
Write on both sides of the answer paper
Answer THREE from the available five questions
All questions carry equal marks
Allocation of marks within each question is shown in brackets
You have TWO HOURS to complete the paper
FIN7028/MAY2017
Answer THREE (3) from the available FIVE (5) questions.
Explicitly state any assumptions you make and any formulas you use in each of your

Question 1
A) How would you test if a process follows a White Noise? Suggest a test statistic and
explain it.
(25 marks)
B) Write an ARMA(p,q) model using three representations. Discuss their importance and
interpretation.
(50 marks)
C) Is there a special characteristic of the process illustrated in the following figure? How
would you model it?
(10 marks)
0
1
0
2
0
3
0
4
0
s
4
0 100 200 300 400 500
t

D) You are given the following Autocorrelation and Partial Autocorrelation STATA output for
the first 12 lags. Write the equation of the model (or models) you would fit to the underlying
time series and explain your reasoning.
-1 0 1 -1 0 1
LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor]
-------------------------------------------------------------------------------
1 0.7084 0.7086 252.41 0.0000 |----- |-----
2 0.7353 0.4694 524.95 0.0000 |----- |---
3 0.6991 0.2347 771.76 0.0000 |----- |-
4 0.6152 -0.0446 963.26 0.0000 |---- |
5 0.6014 0.0112 1146.6 0.0000 |---- |
6 0.5361 -0.0401 1292.6 0.0000 |---- |
7 0.4963 -0.0228 1418.1 0.0000 |-- |
8 0.4476 -0.0412 1520.3 0.0000 |- |
9 0.3978 -0.0411 1601.2 0.0000 | |
10 0.3836 0.0481 1676.5 0.0000 | |
(15 marks)
End of Question 1
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FIN7028/MAY2017

Question 2
A) What is an Impulse Response Function (IRF) and how is it used?
(25 marks)
B) Assuming you fit a model of your choice. What two residual diagnostics would
you use?
(40 marks)
C) Discuss the following Impulse Response Function (IRF) figures.
(35 marks)
Figure 1
0
.5
1
0 50
asymp, rt, rt
95% CI impulse response function (irf)
step
Graphs by irfname, impulse variable, and response variable

Figure 2
-.5
0
.5
1
0 50
asymp, rt, rt
95% CI impulse response function (irf)
step
Graphs by irfname, impulse variable, and response variable

Figure 3
-.5
0
.5
1
0 50
asymp, rt, rt
95% CI impulse response function (irf)
step
Graphs by irfname, impulse variable, and response variable

Figure 4
-1
-.5
0
.5
1
0 50
asymp, rt, rt
95% CI impulse response function (irf)
step
Graphs by irfname, impulse variable, and response variable

End of Question 2
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FIN7028/MAY2017

Question 3
i. Write the equation to describe an AR(1) process. Explicitly state any assumptions
you might make.
ii. What is the mean of this process?
iii. What is the variance of this process?
iv. When is such a process stationary?
(40 marks)
i. What is a nonstationary process?
ii. Fully discuss a statistic to test if a series has a unit root.
(30 marks)
C) You are given the following STATA output for a time series Yt.
------------------------------------------------------------------------------
| OPG
x | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x |
_cons | .0638859 .0809849 0.79 0.430 -.0948416 .2226134
-------------+----------------------------------------------------------------
ARMA |
ar |
L1. | -.2984583 .0933253 -3.20 0.001 -.4813725 -.1155441
L2. | -.0926419 .0794731 -1.17 0.244 -.2484063 .0631225
L3. | -1.073482 .0699466 -15.35 0.000 -1.210575 -.9363896
L4. | .1343098 .0923316 1.45 0.146 -.0466569 .3152765
L5. | -.0441516 .0494018 -0.89 0.371 -.1409774 .0526743
L6. | -.5001629 .0449697 -11.12 0.000 -.5883018 -.412024
|
ma |
L1. | 1.172461 .1059787 11.06 0.000 .9647467 1.380176
L2. | 1.37105 .1556337 8.81 0.000 1.066014 1.676087
L3. | 1.224464 .1945243 6.29 0.000 .8432031 1.605724
L4. | .6371695 .1930177 3.30 0.001 .2588618 1.015477
L5. | .2859264 .1483375 1.93 0.054 -.0048098 .5766626
L6. | -.2640845 .0946195 -2.79 0.005 -.4495354 -.0786337
-------------+----------------------------------------------------------------
/sigma | .9416276 .0319045 29.51 0.000 .879096 1.004159
------------------------------------------------------------------------------

Write the model which is suggested by the above output. Explicitly state any assumptions
you might make.
(30 marks)
End of Question 3
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FIN7028/MAY2017

Question 4
A) Consider you have a time series, rt. Answer the following questions.
i. Write the equations to describe a random walk with and without drift. Explicitly state
any assumptions you might make.
ii. What is the importance of the drift parameter?
iii. What is the 5-steps ahead and 105-steps ahead forecasts implied by the model
without the drift?
iv. Is drift an important factor in financial time series (i.e. stock prices)?
(40 marks)
B) You have a time series, yt, which you need to model. Answer the following questions.
i. First, you perform an Augmented Dickey-Fuller test which yields the output below.
---------- Interpolated Dickey-Fuller ---------
Test 1% Critical 5% Critical 10% Critical
Statistic Value Value Value
------------------------------------------------------------------------------
Z(t) -12.278 -3.440 -2.870 -2.570
------------------------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.0000

Which transformation will you take for your series?

ii. Then, you specify a model, estimate it and obtain the residuals. You examine the
autocorrelation function (ACF) of the residuals and you find the following estimates.

How do you proceed?
(20 marks)

Page 5 of 7
FIN7028/MAY2017

C) You are provided with the following STATA output. What model is employed? Comment
on the relationships between the variables.
(40 marks)
------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
uk |
uk |
L1. | .3891385 .0906135 4.29 0.000 .2115393 .5667378
L2. | .0592089 .0896294 0.66 0.509 -.1164616 .2348793
|
us |
L1. | .049665 .0883177 0.56 0.574 -.1234344 .2227645
L2. | .0160367 .0909355 0.18 0.860 -.1621937 .1942671
|
ca |
L1. | .1042349 .0952222 1.09 0.274 -.0823972 .2908669
L2. | .1100174 .0848875 1.30 0.195 -.0563591 .2763939
|
_cons | .0012729 .0007097 1.79 0.073 -.000118 .0026638
-------------+----------------------------------------------------------------
us |
uk |
L1. | .490393 .1020039 4.81 0.000 .290469 .6903169
L2. | -.3115908 .1008961 -3.09 0.002 -.5093435 -.1138381
|
us |
L1. | .2348676 .0994194 2.36 0.018 .0400091 .4297261
L2. | .0873776 .1023664 0.85 0.393 -.1132568 .288012
|
ca |
L1. | .2398951 .1071919 2.24 0.025 .0298028 .4499873
L2. | -.1317754 .0955581 -1.38 0.168 -.3190658 .0555151
|
_cons | .0029139 .0007989 3.65 0.000 .0013481 .0044796
-------------+----------------------------------------------------------------
ca |
uk |
L1. | .3534272 .0924013 3.82 0.000 .1723239 .5345304
L2. | -.1913663 .0913978 -2.09 0.036 -.3705027 -.0122299
|
us |
L1. | .4682664 .0900601 5.20 0.000 .2917517 .644781
L2. | -.0082187 .0927297 -0.09 0.929 -.1899655 .1735282
|
ca |
L1. | .3378001 .0971009 3.48 0.001 .1474858 .5281144
L2. | -.1758988 .0865623 -2.03 0.042 -.3455579 -.0062397
|
_cons | .0012444 .0007237 1.72 0.086 -.000174 .0026628
------------------------------------------------------------------------------

End of Question 4

Page 6 of 7
FIN7028/MAY2017
Question 5
i. What is the order of integration of a stationary long memory process?
ii. What is the order of integration of a nonstationary long memory process?
iii. Write the general equations which could describe an ARCH(m) model. Explicitly
state any assumptions you would make.
(40 marks)
B) Consider an ARMA(1,3) process. What are the stationarity conditions?
(15 marks)
I. What is the i.i.d. bootstrap?
II. When should we use block bootstrap?
(15 marks)
D) Based on the following STATA output, write the equation for and explain the
fitted model.
(30 marks)
Sample: 1957m2 - 2013m12 Number of obs = 683
Distribution: Gaussian Wald chi2(.) = .
Log likelihood = -1934.459 Prob > chi2 = .
------------------------------------------------------------------------------
| OPG
sp | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
sp |
_cons | .6096803 .1566118 3.89 0.000 .3027269 .9166337
-------------+----------------------------------------------------------------
ARCH |
arch |
L1. | .1213892 .0267218 4.54 0.000 .0690154 .173763
|
garch |
L1. | .8361481 .0286658 29.17 0.000 .7799641 .892332
|
_cons | .9092731 .3228682 2.82 0.005 .2764631 1.542083
------------------------------------------------------------------------------

END OF EXAMINATION

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