ECON41615 Econometrics II 2021
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ECON41615
Econometrics II
2021
Section A
Question 1
Q1.1. Give a short answer for each of the following:
(a.) Describe Perronís procedure and discuss why we need it.
[20 marks]
(b.) What is a spurious regression?
[10 marks]
(c.) What are the (potential) advantages of the Johansen approach over the Engel-
Granger approach when studying possible relations between three time-series that each have one unit root?
[20 marks]
(d.) What is meant by the statement ìxt and yt are cointegratedî?
[20 marks]
Q1.2. Let yt and xt be I(1) random variables, where
yt = 3 + 0:8xt + "t
and "t is I(0), and let the following relationship hold
yt = 5:8 + 0:4yt一1 + 1:3xt - 0:82xt一1 + ut
where ut is I(0) and E (ut ) = 0. Write an error correction model implied by these two equations.
[30 marks]
Question 2
Consider the following process
yt = 0:5 + 0:8yt一1 + "t ;
where "t are independent and identically distributed N(0;7 e(2) = 4):
(a.) Is the model in (1) stable?
[25 marks]
(b.) Rewrite the model (1) in a moving average form.
[25 marks]
(c.) Compute the mean and the variance of yt :
[25 marks]
(d.) Compute the Örst two autocorrelation coe¢ cients of yt : ok , k = 1; 2.
[25 marks]
Section B
Question 3
Consider the following model:
yt = ( )xt + et ; (2)
where et are independent and identically distributed N(0;7 
) and xt is an exogenous variable.
(a.) Classify the process in (2) and determine if it is stable.
[20 marks]
(b.) Calculate the multiplier impact or the short-run multiplier, m0 .
[20 marks]
(c.) Compute the impact on the endogenous variable at time t (yt ) of a unit change in the exogenous variable at time t - 2 (xt一2 ).
[20 marks]
(d.) Calculate the total multiplier or the long-run multiplier, m7 .
(e.) Calculate the mean and median lags.
Question 4
Consider the following bivariate (=two dimensional) VAR(2) model:
[20 marks]
[20 marks]
wt = u + ●1wt一1 + ●2wt一2 + "t t = 1; 2;:::;T
where wt = (xt ;yt )/ and "t ～ i:i:d:N(0; 9):
(a) State the conditions for weak stationarity of this model.
[20 marks]
(b) Suppose that there is one cointegrating relationship. Rewrite the VAR(2) model as a VECM that reáects that there is exactly one cointegrating relationship. DeÖne your notation.
[20 marks]
(c) Suppose that one of the variables, letís say yt , is weakly exogenous with respect to the cointegrating vector. How does your model change?
[20 marks]
(d) What is the di§erence between a time series with a deterministic trend and a time series with a stochastic trend? Describe a method that allows you to distinguish between both possibilities.
[40 marks]
Section C
Question 5
Bera and Higgins (Journal of Economic Surveys, 1993) estimated the following simple model for log (continuously compounded) US$/£ returns rt between January 1973 and June 1985 (T = 651 weekly observations):
t = -0:05 + 0:27rt一1 + 0:003rt一2 - 0:08rt一3
(0.04) (0.05) (0.05) (0.04)
with a GARCH(1,1) speciÖcation for the conditional variance ht of the regression errors ut :
ht = 0:09 + 0:17ut(2)一1 + 0:77ht一1
Numbers in parentheses are estimated (asymptotic) standard errors.
(a) Derive a formula for the 2-step ahead forecast of the volatility of rt .
[50 marks]
(b) Outline one extension of the GARCH(1,1) model that allows for possible asymmetries in the response of volatility to positive and negative shocks.
[50 marks]
2022-04-22