MBFZ05_2017_assignment1
- 格式：pdf
- 大小：310.73 KB
- 文档页数：2
Name: Student number:
Class: MBFZ05 – Research Methodology
Assignment 1
Instructions: This assignment is due in Week 6. Hand in your work in your class in
week 6 (3/13-3/17). For example, if your class is on Monday, you must hand in your
work in the class on 13 March. No extensions will be given, and late assignments will
receive no credit. If you have a university approved excuse for not handing in this
assignment, then your marks for your final exam will be weighted up by 5% to
compensate for the missed work.
You don’t need to necessarily type your answers, but they must be legible and easy
to follow. Answers should be in sentence form (i.e. single word or single number
answers without explanation will be considered incomplete), but clarity of
presentation is important, so try to make your comments/discussion brief and to the
point.
Q1. Suppose 𝑦𝑡 is generated by an MA(1) process, such that 𝑦𝑡=−0.5𝑢𝑡−1+𝑢𝑡; 𝑢𝑡~𝑊𝑁(0,𝜎2)
(a) Is the above MA(1) process invertible?
(b) If the above MA(1) process is invertible, write down its corresponding AR(∞)
representation. What does this imply about the partial autorelation function?
(c) What is the autocorrelation function would look like for the above MA(1)
process? Derive the autocorrelation function.
Q2. Suppose 𝑦𝑡 is generated by an AR(1) process, such that 𝑦𝑡=0.2+0.5𝑦𝑡−1+𝑢𝑡; 𝑢𝑡~𝑊𝑁(0,𝜎2)
(a) What is the partial autocorrelation function of the above AR(1) process?
(b) Is the above AR(1) process stationary?
(c) Derive E(𝑦𝑡)?
(d) Derive V(𝑦𝑡)?
(e) What is the autocorrelation function of the above AR(1) process?
Q3. Suppose 𝑦𝑡 is generated by an ARMA(2,2) process, such that 𝑦𝑡=𝑦𝑡−1−0.25𝑦𝑡−2+𝜀𝑡−𝜀𝑡−1+0.25𝜀𝑡−2; 𝜀𝑡~𝑊𝑁(0,𝜎2)
(a) Suppose we write the ARMA(2,2) process ϕ(L)𝑦𝑡=𝜃(𝐿)𝜀𝑡
how to define ϕ(L) and 𝜃(𝐿)?
(b) Is this ARMA(2,2) process invertible and stationary? Q4. The following question needs to be done using Eviews using the
Fisher_update.XLS. First load the data into Eviews.
(a) In EViews, generate the inflation rate as: INF=400×(log(P(1))−log(P)).
When we construct the inflation rate this way, we lose the last observation,
namely, 2012Q2. We change the sample to 1984Q1 to 2012Q1, which is the
post-float period of the exchange rate. To do this, click on Quick/Sample, type in
the box, which says sample range pairs, 1984Q1 2012Q1, click OK. Then, in the
workfile window, double-click on INF. In the INF window that appears, click
View/Graph/Line (show the figure).
(b) In the INF window, click View/Correlogram (Select Level and 16 lags). This will
give you the correlogram of INF. Comment on which ARMA models would fit the
data.
(c) Estimate the models you considered in (b). Then select one model by using AIC
and SBIC. For example, to estimate an ARMA(2,1) model, click on Object/New
Object/Equation, ok, slect model LS and in the large box that appears type in inf c
ar(1) ar(2) ma(1), in the sample box, type in 1984Q1-2012Q1, then OK.
