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ions for Econometrics 1 a) What is meant by marginalisation and conditioning in the process of model reduction within the dynamic modelling tradition?...

Suppose both X and Y are I(1) variables which are generated by the following true system

Xt=a+bYt+et

Yt=Yt-1+vt

Where e and v are stationary error processes.

a) Define the common stochastic trend underlying this model (20%)
b) What is the cointegrating vector(20%)
c) Explain the relationship between the number of cointegrating vectors in a system and the number of stochastic trends.(20%)
d) What is the importance of the Granger Representation theorem to practical modelling?(40%)

Sample Exam Questions for Econometrics 1 a) What is meant by marginalisation and conditioning in the process of model reduction within the dynamic modelling tradition? (30%) b) Having derived a model for the exchange rate s t as a function of the interest rate differential r t and performed the following regression. s t = a + b r t + e t Where e t is an error term. How would you check for the presence of serial correlation in the error term and how would you deal with it. (30%) c) Explain what recursive estimation is and how it would be used to assess the stability of this equation. (40%) 2 a) Define the term’s weak stationarity, Integrated of order one and uniform mixing. How would you asses the stationarity of a variable X.(30%) b) Suppose X was the US stock market index and your data period was from 1920-1938 (to include the stock market crash). How would the testing procedure for stationarity be affected? (30%) c) If both the Dollar/Sterling exchange rate (E) and the Yen/Dollar exchange rate (Y) were I (1) but there was in fact no relationship between the two variables, what would you expect the result would be of performing the following regression. (40%) E t =a + bY t +v t 3 Suppose both X and Y are I(1) variables which are generated by the following true system X t =a+bY t +e t Y t =Y t-1 +v t Where e and v are stationary error processes.
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a) Define the common stochastic trend underlying this model (20%) b) What is the cointegrating vector(20%) c) Explain the relationship between the number of cointegrating vectors in a system and the number of stochastic trends.(20%) d) What is the importance of the Granger Representation theorem to practical modelling?(40%) 4 Suppose we are estimating a model for the return on a bond r t of the form, r t =a + br t-1 + e t where e is an error term. a) Explain the difference between the conditional variance and the unconditional variance of r. Which of the two is more relevant for financial decision making? (20%) b) If we suspect that the variance of e changes systematically through time what would be the consequences for standard OLS estimation. Outline the ARCH and GARCH models, which would allow us to deal with this problem fully. (30%) c) If you believed that the variance of e affects the return on the bond how would adapt the GARCH model to allow for this. (30%) e) If you were investigating a model such as the capital asset pricing model which used the covariance between the market return r m and the bond return r, How could the GARCH model be extended to allow for this case? (20%) 5 a) Define the components, which make up an ARIMA model. (20%) b) Why is Wolds decomposition fundamental to time series modelling? (20%) c) Outline the Box-Jenkins identification methodology. (30%) d) Define the exponentially weighted moving average time series forecasting approach and give examples of commonly used versions of this model. (30%)
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