Question

2. (15 Marks) You set out to forecast the unemployment rate in the United States (UrateUS), using quarterly data from 1960, first quarter, to 1999, fourth quarter. a) The following table presents the first four autocorrelations for the United States aggregate unemployment rate and its change for the time period 1960 (first quarter) to 1999 (fourth quarter). First Four Autocorrelations of the U.S. Unemployment Rate and Its Change, 1960:I – 1999:IV Lag | Unemployment Rate | Change in Unemployment Rate 1 | 0.97 | 0.62 2 | 0.92 | 0.32 3 | 0.83 | 0.12 4 | 0.75 | -0.07 Explain briefly what these two autocorrelations measure. (3 Marks) b) The accompanying table gives changes in the United States aggregate unemployment rate for the period 1999:I-2000:I and levels of the current and lagged unemployment rates for 1999:I. First Quarter 1999 to First Quarter 2000 Quarter | Unemployment Rate | First Lag | Change in Unemployment Rate 1999:I | 4.3 | 4.4 | -0.1 1999:II | | | 0.0 1999:III | | | -0.1 1999:IV | | | -0.1 2000:I | | | -0.1 Please provide the missing unemployment rate levels for 1999:II to 2000:I. (3 Marks) c) You decide to estimate an AR(1) in the change in the United States unemployment rate to forecast the aggregate unemployment rate. The sample is 1960:I to 1999:IV. The result is as follows: ?UrateUS_t = -0.003 + 0.621 (0.022) (0.106) x ?UrateUS_{t-1}, R^2 = 0.393, SER = 0.255. Using your answers from part b), what is your forecast for the unemployment rate level in the first quarter of 2000? What is the forecast error? (4 Marks) d) You want to see how sensitive your forecast is to changes in the specification. Given that you have estimated the regression with quarterly data, you consider an AR(4) model. This results in the following output: ?UrateUS_t = -0.005 + 0.603 x ?UrateUS_{t-1} - 0.282 x ?UrateUS_{t-2} (0.022) (0.125) (0.189) + 0.106 x ?UrateUS_{t-3} - 0.276 x ?UrateUS_{t-4}, R^2 = 0.416, SER = 0.253. (0.117) (0.191) Does the AR(4) model yield a better forecast of the aggregate unemployment rate in 2000:I, compared to the AR(1) model? Briefly explain how you would choose between these two specifications. (5 Marks)

          2. (15 Marks) You set out to forecast the unemployment rate in the United States (UrateUS), using quarterly data from 1960, first quarter, to 1999, fourth quarter. a) The following table presents the first four autocorrelations for the United States aggregate unemployment rate and its change for the time period 1960 (first quarter) to 1999 (fourth quarter). First Four Autocorrelations of the U.S. Unemployment Rate and Its Change, 1960:I – 1999:IV Lag | Unemployment Rate | Change in Unemployment Rate 1 | 0.97 | 0.62 2 | 0.92 | 0.32 3 | 0.83 | 0.12 4 | 0.75 | -0.07 Explain briefly what these two autocorrelations measure. (3 Marks) b) The accompanying table gives changes in the United States aggregate unemployment rate for the period 1999:I-2000:I and levels of the current and lagged unemployment rates for 1999:I. First Quarter 1999 to First Quarter 2000 Quarter | Unemployment Rate | First Lag | Change in Unemployment Rate 1999:I | 4.3 | 4.4 | -0.1 1999:II | | | 0.0 1999:III | | | -0.1 1999:IV | | | -0.1 2000:I | | | -0.1 Please provide the missing unemployment rate levels for 1999:II to 2000:I. (3 Marks) c) You decide to estimate an AR(1) in the change in the United States unemployment rate to forecast the aggregate unemployment rate. The sample is 1960:I to 1999:IV. The result is as follows: ?UrateUS_t = -0.003 + 0.621      (0.022) (0.106)      x ?UrateUS_{t-1}, R^2 = 0.393, SER = 0.255. Using your answers from part b), what is your forecast for the unemployment rate level in the first quarter of 2000? What is the forecast error? (4 Marks) d) You want to see how sensitive your forecast is to changes in the specification. Given that you have estimated the regression with quarterly data, you consider an AR(4) model. This results in the following output: ?UrateUS_t = -0.005 + 0.603 x ?UrateUS_{t-1} - 0.282 x ?UrateUS_{t-2} (0.022) (0.125) (0.189) + 0.106 x ?UrateUS_{t-3} - 0.276 x ?UrateUS_{t-4}, R^2 = 0.416, SER = 0.253. (0.117) (0.191) Does the AR(4) model yield a better forecast of the aggregate unemployment rate in 2000:I, compared to the AR(1) model? Briefly explain how you would choose between these two specifications. (5 Marks)

2. (15 Marks) You set out to forecast the unemployment rate in the United States (UrateUS), using quarterly data from 1960, first quarter, to 1999, fourth quarter. a) The following table presents the first four autocorrelations for the United States aggregate unemployment rate and its change for the time period 1960 (first quarter) to 1999 (fourth quarter). First Four Autocorrelations of the U.S. Unemployment Rate and Its Change, 1960:I – 1999:IV Lag | Unemployment Rate | Change in Unemployment Rate 1 | 0.97 | 0.62 2 | 0.92 | 0.32 3 | 0.83 | 0.12 4 | 0.75 | -0.07 Explain briefly what these two autocorrelations measure. (3 Marks) b) The accompanying table gives changes in the United States aggregate unemployment rate for the period 1999:I-2000:I and levels of the current and lagged unemployment rates for 1999:I. First Quarter 1999 to First Quarter 2000 Quarter | Unemployment Rate | First Lag | Change in Unemployment Rate 1999:I | 4.3 | 4.4 | -0.1 1999:II | | | 0.0 1999:III | | | -0.1 1999:IV | | | -0.1 2000:I | | | -0.1 Please provide the missing unemployment rate levels for 1999:II to 2000:I. (3 Marks) c) You decide to estimate an AR(1) in the change in the United States unemployment rate to forecast the aggregate unemployment rate. The sample is 1960:I to 1999:IV. The result is as follows: ?UrateUSt = -0.003 + 0.621 (0.022) (0.106) x ?UrateUSt-1, R^2 = 0.393, SER = 0.255. Using your answers from part b), what is your forecast for the unemployment rate level in the first quarter of 2000? What is the forecast error? (4 Marks) d) You want to see how sensitive your forecast is to changes in the specification. Given that you have estimated the regression with quarterly data, you consider an AR(4) model. This results in the following output: ?UrateUSt = -0.005 + 0.603 x ?UrateUSt-1 - 0.282 x ?UrateUSt-2 (0.022) (0.125) (0.189) + 0.106 x ?UrateUSt-3 - 0.276 x ?UrateUSt-4, R^2 = 0.416, SER = 0.253. (0.117) (0.191) Does the AR(4) model yield a better forecast of the aggregate unemployment rate in 2000:I, compared to the AR(1) model? Briefly explain how you would choose between these two specifications. (5 Marks)

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