I’m working on a economics question and need support to help me learn.Section A (It counts for 40% of the total mark)(Answer one and only one question from Section A)Question 1Q1.1. 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 EngelGranger approach when studying possible relations between three time-series thateach 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, whereyt = 3 + 0:8xt + “tand “t is I(0), and let the following relationship holdyt = 5:8 + 0:4yt 1 + 1:3xt 0:82xt 1 + utwhere ut is I(0) and E (ut) = 0. Write an error correction model implied by these twoequations.[30 marks]Question 2Consider the following processyt = 0:5 + 0:8yt 1 + “t; (1)where “t are independent and identically distributed N(0; 2” = 4):ED01/2021 CONTINUEDUniversity Of Durham Copyrightpage number2Exam code:ECON41615WE01
(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: k, k = 1; 2.[25 marks]Section B (It counts for 40% of the total mark)(Answer one and only one question from Section B)Question 3Consider the following model:yt = ( 1:54 + 3:24L 1 0:4L 0:2L2 )xt + t; (2)where t are independent and identically distributed N(0; 2 ) and xt is an exogenousvariable.
(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 inthe exogenous variable at time t 2 (xt 2).[20 marks]ED01/2021 CONTINUEDUniversity Of Durham Copyrightpage number3Exam code:ECON41615WE01SP(d.) Calculate the total multiplier or the long-run multiplier, mT .[20 marks](e.) Calculate the mean and median lags.[20 marks]Question 4Consider the following bivariate (=two dimensional) VAR(2) model:wt = + 1wt 1 + 2wt 2 + “t t = 1; 2; :::; Twhere wt = (xt ; yt)0 and “t i:i:d:N(0; ):
(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 asa VECM that reáects that there is exactly one cointegrating relationship. DeÖne yournotation.[20 marks]
(c) Suppose that one of the variables, letís say yt , is weakly exogenous with respect tothe 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 timeseries with a stochastic trend? Describe a method that allows you to distinguish betweenboth possibilities.[40 marks]Section C (It counts for 20% of the total mark)(Answer all the questions of Section C)Question 5Bera and Higgins (Journal of Economic Surveys, 1993) estimated the following simplemodel for log (continuously compounded) US$/£ returns rt between January 1973 andJune 1985 (T = 651 weekly observations):ED01/2021 CONTINUEDUniversity Of Durham Copyrightpage number4Exam code:ECON41615WE01SPrbt = 0:05 (0:04) + 0:27 (0:05) rt 1 + 0:003 (0:05) rt 2 0:08 (0:04) rt 3with a GARCH(1,1) speciÖcation for the conditional variance ht of the regressionerrors ut: ht = 0:09 (0:03) + 0:17 (0:04) u2t 1 + 0:77 (0:05) ht 1Numbers 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 asymmetriesin the response of volatility to positive and negative shocks.[50 mark
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