# Linear Algorithms for Radioelectric Spectrum Forecast
## 4 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Channel** & **SMAPE-** & **SMAPE-** & **MAPE-** & **MAPE-** & **MAE-** & **MAE-** \\
**Occupancy** & **SARIMA** & **GARCH** & **SARIMA** & **GARCH** & **SARIMA** & **GARCH** \\ \hline Low & \(-\)0.0170 & \(-\)0.0243 & 0.0172 & 0.0247 & 1.6042 & 2.306 \\ Medium & \(-\)0.0470 & \(-\)0.0375 & 0.0466 & 0.0395 & 4.2987 & 3.4385 \\ High & \(-\)0.0488 & \(-\)0.0514 & 0.0497 & 0.0542 & 4.4195 & 4.6565 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Error variables comparison for forecasted values. Figure 16: Availability time of forecasted channels. Figure 17: Occupancy time of forecasted channels. Comparison of performance in forecast is shown in Figure 18, developed on a computer with dual-core processor 2.4 GHz and 4 GB of random access memory (RAM) memory. Here is observed that in general, for each model, the higher the observation time the lower the prediction error. However, this entails no significance. Prediction error is lower in forecast of GARCH algorithms, but a longer observation time in connection to SARIMA algorithm forecast is still necessary. Analyzing the experimental results and considering the best of the cases, the SARIMA algorithm reduces the error to 7.8% when the observation time increases 177.1% for the high occupancy channel. The GARCH algorithm wanes in error about 15.3%, with an increase in the observation time of 128% for the high occupancy channel. In both the ARIMA and GARCH algorithms, a training day to achieve acceptable prediction errors in the three GSM channels is sufficient according to the experimental results. For the analysis of training, Tables 14-16 display the mean squared error for the forecast of reception power for the SARIMA and GARCH algorithms, with up to five days of training data. These results, and Figure 18, suggest that one training day in the SARIMA and GARCH algorithms is sufficient to obtain an acceptable error. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number of** & **SARIMA Mean** & **GARCH Mean** & **SARIMA** & **GARCH** \\
**Training Days** & **Squared Error** & **Squared Error** & **Processing Time** & **Processing Time** \\ \hline
1 & 47.52 & 38.01 & 4.06 s & 8.61 s \\
2 & 45.19 & 38.37 & 4.28 s & 11.15 s \\
3 & 44.94 & 37.15 & 5.36 s & 11.38 s \\
4 & 42.38 & 36.68 & 6.73 s & 14.47 s \\
5 & 41.42 & 36.85 & 8.29 s & 18.55 s \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Result of mean squared error for medium channel with different number of training days. Figure 18: Prediction error vs. Observation time. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number of** & **SARIMA Mean** & **GARCH Mean** & **SARIMA** & **GARCH** \\
**Training Days** & **Squared Error** & **Squared Error** & **Processing Time** & **Processing Time** \\ \hline
1 & 18.64 & 25.48 & 3.88 s & 12.16 s \\
2 & 17.9 & 25.34 & 3.52 s & 18.57 s \\
3 & 18.29 & 24.51 & 4.25 s & 34.38 s \\
4 & 17.53 & 24.82 & 5.92 s & 41.42 s \\
5 & 17.17 & 23.76 & 7.65 s & 55.59 s \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Result of mean squared error for low channel with different number of training days.