Calculators/Sakrekenaars:
Requirements for this paper/Benodigdhede vir hierdie vraestel:
Answer scripts/
Antwoordskrifte:
Yes/Ja
Other resources/Ander hulpmiddels:
Multi-choice cards (A5)/
Multikeusekaarte (A5):
X
Attendance slips (Fill-in paper)/
Presensiestrokies (Invulvraestel):
Multi-choice cards (A4)/
Multikeusekaarte (A4):
Scrap paper/
Rofwerkpapier:
Graph paper/
Grafiekpapier:
Type of assessment/
Tipe assessering:
Small test 2
klein toets 2
Qualification/ BSc
Kwalifikasie:
Module code/
Modulekode:
STTN326
Duration/
Tydsduur:
20 Minutes
20 minute
Module description/
Modulebeskrywing:
Analysis of Dependent Data
Max/
Maks:
15
Examiner(s)/
Eksaminator(e):
Prof Gerrit Grobler
Miss T Mashamba
Date/
Datum:
11/08/2023
Internal/Interne
moderator(s):
Prof Jaco Visagie
Time/
Tyd:
11:00
Submission of answer scripts/Inhandiging van antwoordskrifte:
Ordinary/Gewoon
Question 1
1.1 Define a linear process.
(2)
1.2 Define an AR(p) and an MA(q) process.
(4)
Question 2
Consider the ARMA process
𝑋𝑋𝑡𝑡 =
3
2
𝑋𝑋𝑡𝑡−1 −
1
2
𝑋𝑋𝑡𝑡−2 + 𝑊𝑊𝑡𝑡 + 𝑊𝑊𝑡𝑡−1 − 2𝑊𝑊𝑡𝑡−2 , where
𝑊𝑊𝑡𝑡 is a white noise process 𝑊𝑊𝑊𝑊~(0,1). Identify the process and determine whether it is stationary and/or
invertible.
(5)
Question 3
3.1 Define the AR and MA operators of an ARMA(p,q) process and provide its linear representation.
(2)
3.2 State the problems ARMA(p,q) processes might have that necessitates a check for stationarity and
invertibility?
(2)
TOTAL/TOTAAL: 15
STTN326
1/1