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CPS2509 D.L Sepato et al.
                      Outlier free ARMA (0, 2) - GARCH (1, 1) model forecasts are presented in
                  Figure 2.




















                  Figure 2: Forecast plot for ARMA (0, 2)-EGARCH (1, 1)

                  4.  Discussion and Conclusion
                      The RSME/MSE is lower thus according to Brooks (2008) the forecast with
                  the  smallest  RMSE  and  MAE  provides  the  most  accurate  forecasts.  MAPE
                  shows that the original series is the best since the MAPE value is closest to
                  100. Therefore, SBC and AIC will be used to select the best model. This is a
                  confirmation that outlier free ARMA (2, 2) - EGARCH (1, 1) model is good for
                  the data since it has a small forecasting error. In conclusion, the outlier free
                  data provides good forecasts to predict volatility of JSE top 40 index.

                  References
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                  2.   FOX,A.J. 1972. Outliers in time series. Journal of the Rovail Statistical
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                  3.   CHEN, C. & LIU, L.-M. 1993. Joint estimation of model parameters and
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                  4.   TSAY, R.S. 1988. Outliers. level shifts. and variance changes in time series.
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                  §.   JESUS SANCHEZ, M. AND PENA, D.. 2003. The identification of multiple
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