problem sets

# problem sets - Economics 467 Economic Forecasting...

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Economics 467: Economic Forecasting Department of Economics State University of New York at Binghamton Problem Set #1 (Linear Regression) 1. The fi le entitled MONEYDEM.XLS contains quarterly values of seasonally adjusted U.S.3-month ( TB 3 mo ) and 1-year ( TB 1 yr ) treasury bill rates. Each series is measured over the period 1959:Q3 to 2001:Q1. (a) Plot the time series of each series separately. Does each series appear to have a constant mean and variance over time? (b) Plot each time series on the same fi gure. What can you say about the relationship between the two series? (c) Use Ordinary Least Squares (OLS) to estimate the relationship between long-term and short-term interest rates as TB 1 yr t = α + βTB 3 mo t + ε t (d) What does the estimate of β tell you about the relationship between long-run and short-run interest rates? (e) Test the null that β = 1 . Is this result in accordance with macroeconomic theory? (f) Plot the residuals from the regression in part (c) versus TB 3 mo . Do you observe any pattern? (g) Use the White Test to test for the presence of heteroskedasticity. (h) Estimate the model again, but calculate the robust (White) standard errors. (i) What happens to the coe cients of the model in part (h) relative to part (c)? What happens to the standard errors of the model in part (h) relative to part (c)? Why? (j) Create a dummy variable that is equal to 1 when TB 3 mo is in excess of 10 . 00 and zero otherwise. Include this variable in the regression model as TB 1 yr t = α + βTB 3 mo t + δD t + ε t and run OLS. (k) Test the null that the dummy variable is relevant in part (j). (l) What happens to the fi t of the model in part (j) relative to part (c)? 1

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Economics 467: Economic Forecasting Department of Economics State University of New York at Binghamton Problem Set #2 (ARMA models) 1. The fi le entitled SIM_2.XLS contains simulated data sets. The series Y1, contains ( T = ) 100 values of a simulated AR(1) process. Use this series to perform the following tasks. (a) Plot the sequence against time. Does the series appear to be stationary?
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