CS代考 University of -year Examinations 2016 – cscodehelp代写

University of -year Examinations 2016
Prescription Number(s): STAT317-16S1 / ECON323-16S1
Paper Title:
Time Allowed: Number of Pages:
Time Series Methods
2 hours 3
Instructions for candidate:
 This is a restricted examination
 Only stickered calculators permitted
 Remember to write your name and student
number on all answer booklets/pages  Start each question on a new page
 All questions are equally worth
 Show all working

2 STAT317-16S1/ECON323-16S1
QUESTIONS START ON PAGE 3

QUESTION 1
What are the invertibility and stationarity conditions for an ARMA process? Explain the reasons and the importance for such conditions.
QUESTION 2
Given the moving average process:
x z 0.7z 0.5z z ~N(0,2),
t t t1 t2 t
Find the values  ( k ) of the autocorrelation function for k=1,2,3.
3 STAT317-16S1/ECON323-16S1
QUESTION 3
Identify the order of the following ARMA(p,q) models and determine whether they are causal and/or invertible:
a)
b) wherez
QUESTION 4
Illustrate the major steps of the classical decomposition of a time series.
QUESTION 5
Explain why differencing a time series you remove a deterministic trend and why you should not difference more than twice.
QUESTION 6
Show that an invertible MA(k) model for any integer value of k is equivalent to an AR of infinite order and that a causal AR(k) model for any integer value of k is equivalent to a MA of infinite order.
t
xt  0.8xt1  0.15 xt2  zt  0.3zt1 ; xt  xt1  0.5xt2  zt  zt1 ;
~ N (0, 2 ) . Please show all your workings.
END OF PAPER