MBFZ05_2017_assignment1

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 y t is generated by an MA(1)process, such that

y t=?0.5u t?1+u t; u t~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 y t is generated by an AR(1)process, such that

y t=0.2+0.5y t?1+u t; u t~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(y t)?

(d)Derive V(y t)?

(e)What is the autocorrelation function of the above AR(1)process?

Q3. Suppose y t is generated by an ARMA(2,2)process, such that

y t=y t?1?0.25y t?2+εt?εt?1+0.25εt?2; εt~WN(0,σ2)

(a)Suppose we write the ARMA(2,2)process

?(L)y t=θ(L)εt

how to define ?(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.