## 3 Results
### Best Performing TIs  
Analysing the performances of linear models, on average linear models were the most successful at leveraging the added explanatory power TIs provide. All TIs except the Bandwidth, the COPP, and the ROC successfully reduced LR's RMSE, while all TIs except the Bandwidth reduced HR's RMSE. Out of the TIs that successfully improved the performances of linear models, we found that %B (\(n=58\)) and EMA (\(s=2\)) added the most explanatory power. Per the results in Table 1, across LR and HR models, %B (\(n=58\)) on average reduced the RMSE and MAE by 4.42% and 3.72% respectively, and increased the PCC by 2.91%. EMA (\(s=2\)) improved the same metrics on average by 4.13%, 5.48%,  
\begin{table}
\begin{tabular}{l l l l l l l l l l l l} \hline  & & **LR** & **HR** & **RF** & **AB** & **GB** & **2 NN** & **CNN** & **2 CNN** & **2 CNN\_NN** & **ResNet** \\ \hline \multirow{8}{*}{**TIS**} & **TI** & \%B & EMA & EMA & MOM & MOM & EMA & ROC & ROC & ROC & ROC \\  & **HP** & n = 58 & s = 2 & s = 6 & n = 58 & n = 22 & n = 49 & n = 49 & n = 9 & n = 27 \\  & **RMSE** & 11.47 & 15.12 & 12.66 & 11.64 & 10.96 & 11.14 & 11.03 & 11.10 & 11.09 \\  & **\%RMSE** & 4.49 & 4.50 & 1.66 & 5.42 & 7.34 & 4.09 & 2.73 & 2.39 & 2.36 & 1.38 \\  & **MAE** & 7.87 & 7.67 & 8.07 & 8.58 & 7.84 & 7.59 & 7.65 & 7.58 & 7.66 & 7.56 \\  & **\%MAE** & 3.26 & 5.59 & 2.10 & 6.20 & 2.22 & 1.56 & 4.21 & 2.91 & 3.41 & 1.75 \\  & **\%CC** & 0.79 & 0.79 & 0.76 & 0.74 & 0.79 & 0.81 & 0.80 & 0.81 & 0.81 & 0.80 \\  & **\%FCC** & 2.92 & 2.75 & 1.08 & 3.79 & 2.80 & 1.85 & 1.40 & 1.19 & 0.95 & 0.82 \\  & **DM** & **10.39** & **14.86** & 1.74 & **4.18** & **3.68** & **3.23** & **7.15** & **4.51** & **5.15** & **4.28** \\ \hline \multirow{8}{*}{**TIS**} & **TI** & EMA & \%B & MOM & ROC & \%B & SMA & - & EMA & SMA & COPP \\  & **HP** & s = 2 & n = 58 & n = 58 & n = 57 & n = 54 & n = 22 & - & s = 18 & n = 18 & * \\  & **RMSE** & 11.57 & 11.59 & 12.22 & 11.71 & 11.78 & 11.08 & - & 11.26 & 11.27 & 11.16 \\  & **\%RMSE** & 3.45 & 1.57 & 5.01 & 2.66 & 3.00 & - & 0.37 & 0.91 & 0.77 \\  & **MAE** & 7.70 & 7.78 & 8.15 & 8.68 & 7.81 & 7.68 & - & 7.77 & 7.78 & 7.60 \\  & **\%MAE** & 5.36 & 4.17 & 1.10 & 5.14 & 2.60 & 1.56 & - & 0.44 & 1.91 & 1.16 \\  & **FCC** & 0.79 & 0.79 & 0.77 & 0.73 & 0.78 & 0.81 & - & 0.80 & 0.80 & 0.80 \\  & **\%FCC** & 2.55 & 2.89 & 1.57 & 3.23 & 1.71 & 1.38 & - & 0.06 & 0.01 & 0.40 \\  & **DM** & **13.67** & **12.30** & 1.23 & **4.36** & 1.61 & 2.08 & - & 0.16 & 1.36 & **2.40** \\ \hline \multirow{8}{*}{**TIS**} & **TI** & 'Histogram’ & SMA & ROC & EMA & EMA & ’Histogram’ & - & - & COPP & - \\  & **HP** & **n = 18 & n = 57 & s = 6 & s = 6 & ** & ** & ** & ** & ** & ** \\  & **RMSE** & 11.66 & 12.63 & 12.82 & 12.79 & 11.12 & - & - & 11.28 & - \\  & **\%RMSE** & 3.25 & 3.76 & 1.50 & 4.19 & 2.53 & 2.66 & - & - & 0.75 & - \\  & **MAE** & 7.88 & 7.79 & 8.18 & 8.78 & 7.84 & 7.68 & - & - & 7.78 & - \\  & **\%MAE** & 3.11 & 4.02 & 0.77 & 4.06 & 2.20 & 1.51 & - & - & 1.89 & - \\  & **PCC** & 0.79 & 0.79 & 0.76 & 0.73 & 0.7 and 2.65% respectively. Analysing %B and EMA linear model performances across different target groups, Table 2 highlights that both %B (\(n=58\)) and EMA (\(s=2\)) significantly reduced a majority of tail forecast errors, without, however, improving IQR forecasts. Specifically, %B (\(n=58\)) and EMA (\(s=2\)) yielded both negative tail \(\tilde{\text{W}}+\tilde{\text{L}}\) and %Ws greater than 50%: 55.79% and 60.10%. Neither TI, however, yielded a negative \(\tilde{\text{W}}+\tilde{\text{L}}\) for targets inside the IQR. Moreover, only EMA (\(s=2\)) successfully reduced a majority (53.35%) of IQR forecast errors. Examining the performances of ensemble models, in Table 1, TIs recorded statistically significant reductions in forecast error with two out of three ensemble models. EMA (\(s=6\)) was the only _best TI_ to not yield a statistically significant performance improvement. It nonetheless reduced RF's RMSE and MAE by 1.66% and 2.10% respectively, and increased its PCC by 1.08%.