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ARMA modelling of the forward premium: Box Jenkins methodology and forecasting.
The objectives of this seminar are to:
• Identify, estimate and test an ARMA model for the forward premium (Box-Jenkins methodology).
代写留学生论文• Forecast the forward premium using this ARMA model and using the CIP (structural) model estimated in Seminar 3.
• Evaluate the forecasts from both models to see which provides better out-of-sample forecasts of the forward premium.
The learning outcomes from this seminar will be to develop your understanding of:
• ARMA modelling (identification, estimation and testing) and forecasting in Eviews.
• Forecast evaluation.
• The utility of ARMA models as forecasting tools.
The analysis is carried out in this handout for models of the forward premium (using the same workfile, cip_sem3.wf1, as used in Seminar 3). Try carrying out a similar analysis in your own time comparing the forecasts from a structural model of the 3 month holding period returns on sterling (UIP) with those from an ARMA model of this variable.
We are going to estimate the models for the period 5/09/2001 – 9/30/2004. Then we are going to ()Tt,...,1=forecast the forward premium out of sample for the period 10/1/2004 – 9/30/2005(). t=1 t=T t=T+1 t=T+H In sample estimation period Out of sample forecast period
1. Forecasting with the CIP model
Firstly we need to re-estimate the GMM CIP model (see seminar 3) for the in sample estimation period 5/09/2001 – 9/30/2004.
Open the equation cip_gmm (which you saved in the last seminar) and click Estimate on the equation toolbar. Change the Estimation settings/sample to: 5/09/2001 – 9/30/2004. Then click OK.
Now forecast the forward premium for the period 10/1/2004 – 9/30/2005.
Click Forecast on the equation toolbar. Change the Forecast sample to: 10/1/2004 – 9/30/2005. Click OK: -.01.00.01.02.032004M102005M012005M042005M07FP_3MFForecast: FP_3MFActual: FP_3MForecast sample: 10/01/2004 9/30/2005Included observations: 261Root Mean Squared Error 0.004045Mean Absolute Error 0.003422Mean Abs. Percent Error 26.21858Theil Inequality Coefficient 0.138642 Bias Proportion 0.560762 Variance Proportion 0.049786 Covariance Proportion 0.389452
Freeze this forecast view for comparison later with the ARMA model forecasts:
Click freeze on the equation toolbar. Then name the resulting graph: cip_fcast
These forecasts are static forecasts. These forecasts are made using the:
• Actual values of the explanatory variables (in this case, the interest differential) in the forecast period.
• Estimated coefficients from the in-sample estimation period ()βˆ :
HhxyhThT,...,1 ,ˆˆ=′=++β
The forecast error is given by:
()ββεβεβˆˆˆˆ−′+=′−+′=−≡++++++++hThThThThThThTShTxxxyye
The forecast error depends on both residual uncertainty (the first term) and parameter uncertainty (the second term).
The forecast error variance is therefore:
()()()[]()hThThThThTShTxXXxxxe+−+++++′′+=′+=121ˆvarvarˆvarσβε
From the above, a 95% forecast interval is given by:
()ShThTey++±ˆvar96.1ˆ
The point forecasts ( and the 95% forecast interval are plotted in the Eviews output. hTy+ˆ
Forecast evaluation (see Brooks 5.12.8 and Eviews help index under ‘Forecast, interval’)
What is the total amount of error associated with the forecast? A forecast with a smalle