Consider the following ARMA(1,1) model for some time series data

Problem 1 (35 marks). Consider the following ARMA(1,1) model for some time series data yt = 0.036 + 0.691,:t1 + 0.42m_1 + to Suppose that you have data for time to t 1, ie you know that ytl = 3.4 , and no-1 = 1-3 a) Obtain forecasts for the series y for times at, 12+ 1, and 13+ 2 using the estimated ARMA model- [8 marks] 1)) If the actual values for the series turned out to be -0.032, 0.961, 0.203 for t, t + 1, t + 2, calculate the (outofsample) mean squared error, mean absolute error and percentage of correct sign predictions. Comment on the differing characteristics of the three methods used for evaluating the forecasting accuracy. [12 marks] c) 'What procedure might be used to estimate the parameters of an ARMA model? Ex- plain, briey, how such a procedure operates, and why OLS is not appropriate. [5 marks] d) Suppose that we nd ARCH effects in the data and use a GARCH model to capture the dependence structure in the variance. What procedure might be used to estimate the parameters of a GARCH model? Explain, briey, how such a procedure operates, and why OLS is not appropriate. Also comment on the possible problems of the procedure you suggest. [10 marks]