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### Miderm 2

Course: ECON 467, Fall 2011
School: Binghamton
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467: Economics Economic Forecasting State University of New York at Binghamton Department of Economics Spring 2010 Midterm II The exam consists of three questions on two pages. Each question is of equal value. 2 1. Consider the model yt = c + yt1 + t + t1 , where t W N 0, 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...

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467: Economics Economic Forecasting State University of New York at Binghamton Department of Economics Spring 2010 Midterm II The exam consists of three questions on two pages. Each question is of equal value. 2 1. Consider the model yt = c + yt1 + t + t1 , where t W N 0, 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 H0 : = 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 2 2. Consider the model yt = + xt + t , where both t W N 0, and xt W N 0, x are white noise sequences. Assuming that t and xt are uncorrelated and that the parameters of the model are known (a) Find the h-step ahead forecast for h = 1, 2, . . .. (b) Find the h-step ahead forecast error for h = 1, 2, . . .. (c) Find the h-step ahead forecast error variance for h = 1, 2, . . .. (d) Find the h-step ahead interval forecast for h = 1, 2, . . .. (e) Plot parts (a) and (d) in a single gure. 3. Suppose we are interested in modeling the federal funds rate (FFR). FFR is the interest rate at which private depository institutions lend balances at the Federal Reserve to other depository institutions, usually overnight. In other words, it is the interest rate banks charge each other for loans. We have a tenative model in mind and want to perform diagnostic checks to make sure the model is correctly specied. Specically, we wish to conduct a Lagrange Multiplier (Raos Score) Test. To do so, consider the two EViews regression output tables listed below. (a) Write out the null hypothesis for this test. (b) Give the test statistic (both and with without numbers) for this test as well as note its distribution. (c) If you fail to reject the null of this test, what do you conclude? (d) If you reject the null of this test, what do you conclude? (e) What is the next step in the Box-Jenkins methodology for parts (c) and (d)? 1 Dependent Variable: FFR Sample (adjusted): 1960Q3 2005Q3 Included observations: 181 after adjustments Convergence achieved after 54 iterations Backcast: 1960Q1 1960Q2 Variable Coefficient Std. Error t-Statistic Prob. C AR(1) AR(2) MA(1) MA(2) 6.132360 0.682867 0.241307 0.606427 -0.045276 1.432081 0.471074 0.432481 0.473688 0.229946 4.282132 1.449597 0.557961 1.280225 -0.196898 0.0000 0.1490 0.5776 0.2022 0.8441 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 0.923025 0.921276 0.936499 154.3573 -242.4178 2.002453 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic) 6.155470 3.337739 2.733898 2.822255 527.6141 0.000000 Dependent Variable: FFR Sample (adjusted): 1960Q3 2005Q3 Included observations: 181 after adjustments Convergence achieved after 39 iterations Backcast: 1959Q1 1960Q2 Variable Coefficient Std. Error t-Statistic Prob. C AR(1) AR(2) MA(1) MA(2) MA(3) MA(4) MA(5) MA(6) 6.187277 0.444451 0.289135 0.864227 0.311643 0.315123 0.336925 0.433578 0.398218 0.923243 0.186926 0.177090 0.174338 0.122266 0.107523 0.103580 0.101742 0.074247 6.701676 2.377689 1.632700 4.957204 2.548898 2.930739 3.252812 4.261547 5.363396 0.0000 0.0185 0.1044 0.0000 0.0117 0.0038 0.0014 0.0000 0.0000 R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 0.929635 0.926362 0.905738 141.1022 -234.2922 2.035376 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic) 6.155470 3.337739 2.688312 2.847353 284.0499 0.000000
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Binghamton - ECON - 467
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