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Miderm 2

# Miderm 2 - Economics 467 Economic Forecasting State...

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Economics 467: Economic Forecasting State University of New York at Binghamton Department of Economics Spring 2010 Midterm II Theexamcons istso fthreequest ionsontwo pages. Each question is of equal value. 1. Consider the model y t = c + φy t 1 + ε t + θε t 1 ,where ε t WN ¡ 0 2 ε ¢ is a white noise sequence. (a) Write the log-likelihood function needed to estimate this model. (b) Why do we want to maximize the funciton in part (a) as opposed to minimizing a function as we did with OLS? (c) Consider the null hypothesis H 0 : θ = 0. Write the log-likelihood function needed to estimate the model under the null hypothesis. (d) Write the test statistic needed to test the null hypothesis in part (c) as well as note its distribution. (e) Do we know the sign of the test statistic? If so, what is it and why? 2. Consider the model y t = μ + βx t + ε t ,whereboth ε t WN ¡ 0 2 ε ¢ and x t WN ¡ 0 2 x ¢

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Miderm 2 - Economics 467 Economic Forecasting State...

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