Assignment 2
BUSM21
2007-10-01
Model generation
In order to determine an appropriate model for forecasting the index returns (using a Box-Jenkins approach), the return series was plotted in a correlogram (Appendix 1).
The autocorrelation function suggested an inclusion of approximately three Moving Average (MA) variables since the three initial observations seemed significant, and two Autoregressive (AR) variables since the partial autocorrelation motivated such a decision due to its abrupt decay after only two lags.
However, despite the initial belief of the amount of variables to include, several attempts using a different number of variables were conducted before several indications showed that the best combination was the initial belief of ARMA (2,3). The primary reason for this combination was that including additional lags was distorted the function either through being insignificant or by adversely influencing other variables to become insignificant. This model was also supported by the values of the following criteria:
• Akaike info criterion
• Schwarz criterion
• Adjusted R2
The goal was to find the optimal of the above three criteria which are the lowest possible values of Akaike and Schwarz and the highest possible value of R2 adjusted.
Variable Coefficient Std. Error t-Statistic Prob.
C 0.000843 0.000430 1.960178 0.0511
AR(1) 0.214111 0.036626 5.845929 0.0000
AR(2) -0.861320 0.032552 -26.46013 0.0000
MA(1) -0.397775 0.069999 -5.682623 0.0000
MA(2) 1.026098 0.015154 67.70922 0.0000
MA(3) -0.203758 0.069256 -2.942119 0.0036
R-squared 0.106187 Mean dependent var 0.000866
Adjusted R-squared 0.087566 S. ...