Difference between the zero-coupon interest rates

The term spread is defined as the difference between the zero-coupon interest rates on three-month Treasury bills and 10-year Treasury bonds. The data start from January 1957 to March 2015, downloaded from the Federal Reserve Bank of St. Louis FRED at the monthly frequency. Import the Spread.xlsx into Eviews. (1) Using E views, plot the term spread with a line chart and draw a horizontal line at value zero on the graph. Explain why the term spread typically takes a negative value? Hint: to draw the horizontal line, from a graph object, click the Line/Shade Type: Line; Orientation: Horizontal –left axis; Position: Data Value 0. (2) Compute the sample ACF and the sample PACF for this series for the first 12 lags using E views. Comment on the pattern of the correlogram. (3) Consider three models 0 1 1 1 1 0 1 1 2 2 0 1 1 2 2 3 3 Model 1: y Model 2: y Model 3: y                                   t t t t t t t t t t t t t y y y y y y (i) [5 marks] Select the best model using AIC and BIC. Hint: Sample sizes need to be the same when comparing models with AIC or BIC. That is, use the sample period starting from 1957m04 to 2015m03 for the estimation of all three models. (ii) [1 mark] Using Eviews, compute the ACF and PACF (the first 12 lags) of the residual of the preferred model, estimated from the sample running from 1957m04 to 2015m03. (iii) [6 marks] Conduct Ljung-Box Q(5) tests for the residual of the preferred model at the 5% significance level. Hint: Calculate the Ljung-Box Q-statistics by hand (i.e., use the sample ACF obtained from Eviews and show all your working) and show the decision rules used. Compare the forecasting performance of the ARMA(1,1) and AR(3) models. The insample estimation period is 1957M01 to 2012M12 and the out-of-sample forecast period is 2013M01 to 2015M03. (4) [3 marks] What are the similarities and differences between a static and a rolling window one-step-ahead forecast? (5) [3 marks] What are the similarities and differences between a one-step-ahead static and a dynamic forecast? (6) [2 marks] Estimate the ARMA(1,1) and AR(3) models over the period 1957M01 to 2012M12. (7) Use the estimation results of each model in (6) to provide a dynamic forecast for the rest of the sample period. (i) [5 marks] What are the RMSEs? Which model would you select based on the RMSEs of this forecasting method? Attach the Eviews forecast evaluation results. (ii) [3 marks] For the preferred model, plot the original time series, your forecasts and prediction intervals for this period (see tutorial week 10 for an example of the graph) and comment on the forecasting results. (8) Conduct rolling window forecasts based on the ARMA(1,1) and AR(3) models. Specifically, estimate each model over the period 1957m04 to 2012m12; obtain the one-step-ahead forecast and the one-step-ahead forecast error; continue to update the estimate period so as to obtain the 27 one-step-ahead forecast and forecast error. Hint: you could obtain the rolling window one-step-ahead forecasts and forecast errors by revising the Eviews program rolling_forecasting.prg described in Lecture week 9. (i) [6 marks] What are the RMSEs? Which model would you select based on the RMSEs of this forecasting method? Attach the programs in an appendix (at the end of the assignment) and highlight the changes you made to the code. (ii) [3 marks] For the preferred model, plot the original time series, your forecasts and prediction intervals for this period and comment on the forecasting results.                                                  

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