ECO302 Advanced Econometrics
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1st Semester 2022/23
Coursework
ECO302 Advanced Econometrics
Question 1. [40pt]
In the excel sheet, you will find two integers associated with the student number of your group leader for this question. Report this number at the start of your answer (call it a and b), and proceed as follows:
We have an ordered choice model
,． 1
． ． ．
．
．(．) 2
． ．
yi = ． 3
． ．
4
． ． ．
．( 5
y*i = 1.7zi + ei
if y*i ≤ 2
if 2 < y*i ≤ 2.5
if 2.5 < y*i ≤ 3.1
if 3.1 < y*i ≤ 7
if y*i > 7
where ei ~ N (0, 1). We have a second model
y˜*i = 80 + 81zi + 7i
2 if 71 < y˜*i ≤ 72
yi = ． 3 if 72 < y˜*i ≤ 73
．
．
4 if 73 < y˜*i ≤ 74
．
．
．( 5 if y˜*i > 74
where 7i ~ N (0, b).
Set 7a = 0. Find the value of all the rest of the parameters in the second model (in-
cluding 80 , 81 , 71 , 72 , 73 , 74), so that the two models are equivalent.
Question 2. [60pt]
In the excel sheet, you can find four numbers associated with the student number of your group leader for question 2. Use all four of the random numbers as parameters, out of which four being ARMA coefficients (including the intercept) and one being the variance of the random error, and form a stationary lRdl(1, 1) model. (yt = 60 + 61 yt-1 + et + 91et-1 , et ~ i.i.d. (0, 72 ), so four parameters in total.)
(1) Write down your model.
(2) Show that given your choice of parameters, your ARMA model is stationary. (If not, go back to the previous step and reallocate your parameters.)
(3) Find the first three autocovariances 70 , 71 and 72 . Show each of your steps clearly.
(4) Find the general formula for autocovariances. Show each of your steps clearly. (Hint: for (3) and (4), you will need a bit of research on your own. Keyword: Yule- Walker equations. There is one simple illustrative example in the textbook excerpt. The derivations on page 5-6 of the lecture notes follow the same spirit.)
2022-12-28