M3S8
Department of Mathematics
Question
Q 1
Q 2
Q 3
Time Series
Examiner's Comments
Parts (a) and (b) were generally well done, with nearly all getting more than half of the
true/false questions right. Part c was generally done quite well. Part (d) was problematic
with a surprising number of basic errors, such as the covariance of two summation
expressions being written incorrectly. Part (e): quite poorly done even though the bits
required had been worked out in (c) and (d).
The best answered question. (a)(i) was well done. (a)(ii) should have been easy to derive
given (a)(i) but most students missed the simple approach and proceeded to derive s_0,
s_1, s_2 from scratch. While often done correctly this took a LOT of time and effort. Parts
(b)-(d) were generally well done using links between polynomial roots and parameters
and showed good understanding of these structures.
Part 3(a)(i) was standard material and well done. Part (a)(ii) was unseen, and many
students did not attempt it, but those who did often did well. Of those who didn't,
summations were often thoroughly mistreated. Part (b) had elements in common with
previously seen coursework, and was generally quite well done.
This question proved problematic. (a)(i) The idea of setting up a variance to show positive
semidefiniteness was done in an early lecture, but forgotten by many. (a)(ii) Showing joint
stationarity was quite well done although notation was often very poor. (iv) Surprisingly
many defined the coherence incorrectly even though I had emphasized its importance in
class. Quite a few got its value of unity correct, often by guesswork. (v) It was generally
underappreciated that linear correlation being perfect implies a simple relationship
between the variables which should be exploited here. Part (b) was generally well done
with only (b)(iii) causing difficulties to some.
Q 4
Printed: 27/07/2018 11:48:08
M45S8
Department of Mathematics
Question
Q 1
Q 2
Time Series
Examiner's Comments
Parts (a) and (b) were generally well done, with nearly all getting more than half of the true/false
questions right. Part c was generally done quite well. Part (d) was problematic with a surprising
number of basic errors, such as the covariance of two summation expressions being written
incorrectly. Part (e): quite poorly done even though the bits required had been worked out in (c)
and (d).
The best answered question. (a)(i) was well done. (a)(ii) should have been easy to derive given (a)(i)
but most students missed the simple approach and proceeded to derive s_0, s_1, s_2 from scratch.
While often done correctly this took a LOT of time and effort. Parts (b)-(d) were generally well
done using links between polynomial roots and parameters and showed good understanding of
these structures.
Part 3(a)(i) was standard material and well done. Part (a)(ii) was unseen, and many students did not
attempt it, but those who did often did well. Of those who didn't, summations were often
thoroughly mistreated. Part (b) had elements in common with previously seen coursework, and
was generally quite well done.
Q 3
This question proved problematic. (a)(i) The idea of setting up a variance to show positive
semidefiniteness was done in an early lecture, but forgotten by many. (a)(ii) Showing joint
stationarity was quite well done although notation was often very poor. (iv) Surprisingly many
defined the coherence incorrectly even though I had emphasized its importance in class. Quite a
few got its value of unity correct, often by guesswork. (v) It was generally underappreciated that
linear correlation being perfect implies a simple relationship between the variables which should be
exploited here. Part (b) was generally well done with only (b)(iii) causing difficulties to some.
The integration in (a) was mostly well done with odd/even functions being recognized. (b)(i) caused
surprising difficulties in showing m and finding \ell. Many completed (b)(ii) quite well and it was
clear that (b)(iii)-(v) were often not attempted due to time running out.
Q 4
Q 5
Printed: 27/07/2018 11:48:08

欢迎咨询51作业君