## 3 Results
### Generalization Ability of the Proposed Model  
To assess the generalization ability of the proposed model, data from a new time period was considered, and this period commences just after the ending date of the data set on which the final model was built. Same procedure was carried out to prepare the input sets for the three indices AORD, GSPC and ASPI by assuming the input variables remain unchanged for the next three months. Standard PNN and proposed PNN without MCUB and proposed PNN with MCUB were used to forecast the direction of stock indices and results displayed in Table 7 (see page 14).  
By referring to Table 7, it can be seen that the proposed PNN exhibits better performance than the standard PNN before introducing the MCUB technique to both models. The model with MCUB and proposed PNN exhibits higher performance than the other two models for the novel data set. When comparison was done with the performance of same models (proposed PNN with MCUB) for the data set considered in the study and for the data of new time period, a slight decrease in overall accuracy can be observed in AORD and GSPC indices while slight increase of overall accuracy is visible in ASPI index. All the misclassification percentages exhibit similar values when comparing corresponding misclassification percentages of the final proposed PNN model with multivariate scaled t distribution and MCUB technique. Therefore, it can be said that the model proposed by the study is capable of forecasting the direction of a stock market index with an acceptable accuracy.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & & \\ \cline{3-13}
**Market** & **Model** & **Overall** & & & & & & & & & & & & \\ \cline{3-13}  & & & & & & & & & & & & & & \\ \cline{3-13}  & & & & & & & & & & & & & & \\ \hline \multirow{4}{*}{AGRD} & Standard PNN & 52.8738 & 47.1262 & 70.9956 & 5.186 & 60.9506 & 3.4527 & 5.6923 & 67.1429 & 55.2838 & 3.2222 & 1.9638 \\ \cline{2-13}  & Proposed PNN & 60.2089 & 39.7911 & 54.2253 & 7.0492 & 52.1210 & 2.0000 & 5.6923 & 52.2253 & 46.4287 & 4.8270 & 2.2222 \\ \cline{2-13}  & Proposed PNN & 65.9039 & 34.0961 & 36.9672 & 34.9593 & 30.7273 & 2.1429 & 4.0060 & 34.8243 & 26.6667 & 19.2592 & 15.3347 \\ \cline{2-13}  & with MCUB & & & & & & & & & & \\ \hline \multirow{4}{*}{GSTC} & Standard PNN & 50.6645 & 49.3355 & 42.8093 & 24.3969 & 73.6734 & 21.8485 & 26.5252 & 20.39608 & 47.1482 & 9.2857 & 15.1112 \\ \cline{2-13}  & Proposed PNN & 61.3846 & 38.6154 & 49.301 & 15.022 & 47.6741 & 3.9724 & 14.0909 & 45.3266 & 33.5832 & 6.5007 & 8.5183 \\ \cline{2-13}  & Proposed PNN & 65.8981 & 34.1019 & 35.3335 & 32.5110 & 34.4612 & 4.5495 & 2.0000 & 30.7879 & 32.4612 & 14.0588 & 18.4522 \\ \cline{2-13}  & Standard PNN & 55.9072 & 44.0928 & 43.7361 & 24.4219 & 73.7099 & 4.2361 & 16.2253 & 39.5 & 56.9456 & 14.1492 & 10.2727 \\ \hline \multirow{4}{*}{ASFT} & Proposed PNN & 64.0606 & 35.9394 & 39.1781 & 31.1388 & 51.1051 & 3.9528 & 6.9090 & 35.2253 & 44.1961 & 8.2853 & 4.8805 \\ \cline{2-13}  & Proposed PNN & 71.7790 & 28.2210 & 28.3139 & 28.8171 & 27.5319 & 2.2727 & 7.3156 & 26.0412 & 20.2163 & 12.5623 & 16.2548 \\ \cline{1-1} \cline{2-13}  & Proposed PNN & 71.7790 & 28.2210 & 28.3139 & 28.8171 & 27.5319 & 2.2727 & 7.3156 & 26.0412 & 20.2163 & 12.5623 & 16.2548 \\ \cline{1-1} \cline{2-13}  & & & & & & & & & & & \\ \hline \end{tabular}
\end{table}
Table 7: Performance of models for a novel data set.