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CPS1297 Chin W.C. et al.
1
using the equations 2, = ∑ 5 =1 ln( 2, ) and 2,ℎ =
1 2, 5
∑ 522 ln( ).
22 =1

In order to obtain better forecasted results, we combine several
competitive forecasts into a single forecast by forecast averaging methods to
improve our forecast results. We use a few commonly used averaging
weighting (ω) schemes such as the simple-mean (SM), simple median (SMed)
and least squares (LS) approaches.

3. Results and Discussion
This study has selected the Mexico Stock Exchange, which is ranked the
second largest in Latin American stocks. The IPC index indicates the BMV
overall performance. It is made up of a balanced weighted selection of shares
that are representative of all the shares listed on the exchange from various
sectors across the economy. In this study, the in-sample data are started from
January 2010 and ended at 2015 December (1479 days). The forecast
evaluation results are presented in Table 1.

Forecast evaluations
Table 1: Dynamic Forecast Evaluations
Actual: BV Forecast evaluation
Forecast method MAE RMSE MAPE
Individual : HAR(RV)- 0.00005110 0.00021915 95.14545878
TGARCH
HAR(BV)-TGARCH 0.00004161 * 0.00021773 * ** 56.18827691
,
GARCH-t 0.00004781 0.00022120 52.51741209 *
TARCH-t 0.00004969 0.00022159 57.40503898
Average : Simple mean 0.00003892 ** 0.00021801 42.05743195

Simple median 0.00003900 0.00021835 39.40507510 **
Least-squares 0.00004161 0.00021773 ** 56.18828106
Notes: * indicates the smallest (best) value for individual forecast only.
** indicates the smallest (best) value for individual and average forecasts.

Table 1 reports the dynamic forecast evaluations, which consist of 116 days
from July 2015 until December 2015 for MAE, RMSE, and MAPE for the four
models. Using the dynamic forecast approach, the estimated parameters will
be used for the next one-day-ahead forecast. For the overall forecast
evaluations among the individual forecasts and average forecasts, it is found
that almost all the smallest forecast loss functions are dominant by the
average forecasts such as least squares and simple median methods. These

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