a. Consider the following autoregressive process:

Is this process covariance stationary?[5 marks]

b. Consider the process:

Can this ARMA(1,1) process be expressed as an AR process?If so, give the first four terms of the equivalent AR process. [15 marks]

c. Suppose that we had data on the CLP: GBP exchange rate and applied the Augmented Dickey-Fuller test.When testing for a unit root against the alternative of a constant mean we find that we cannot reject the null at the 10% level of significance.When testing for a unit root against the alternative of a deterministic time trend we find that we can reject the null at the 5% level of significance but not at the 1% level of significance.

What would be your conclusion as to the stationarity of the exchange rate series?What implications would this have for the further analysis of the series? [15 marks]

d. Suppose that we have the following estimated distributed lag model:

where y is the weekly change in the three-month interbank lending rate in Canada and x is the weekly change in the three-month interbank lending rate in the USA, both measured in percentage points, and numbers in ( )are the standard errors.

Suppose that both y and x are covariance-stationary.

i)Under what conditions would OLS estimation of this model be consistent?Do you think these conditions would be satisfied?[5 marks]

ii)If the change in the USA three-month interbank lending rate were to increase by one point, what would be the expected effect on the change in the Canadian three-month interbank lending rate?[5 marks]

iii)Outline appropriate tests for serial correlation and heteroskedasticity with respect to the residuals of this regression.[5 marks]

iv)What would be the consequences of error serial correlation and heteroskedasticity in the context of this model?[5 marks]

Suppose that you applied the tests outlined in iii) above and concluded that serial correlation and heteroskedasticity were present.What adjustments would you make to the model and/or estimation?[5 marks]