# Linear Algorithms for Radioelectric Spectrum Forecast
## 4 Results and Discussion  
In Figure 14 an example is displayed where there is application of the designed time series algorithms. Here, the interaction between the CR user and the primary base station (BS) is shown by received power from the primary transmitter. This is represented by the oval and the direction of the arrows. The CR user can forecast the power level it will receive from the primary BS. In the example of Figure 14, in order to analyze the SARIMA and GARCH algorithms, the forecast of the power is performed by the CR user, making a comparison with the spectrum analyzer in which the measurements were made. However, this depends on the architecture of CR deployed in the environment. Due to the processor and power consumption being more limited in the CR user's computer, use of infrastructure architecture is recommended, where the forecast is carried out by the  
Figure 13: Histogram of residuals and normal probability for GSM channels. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Lag**} & \multirow{2}{*}{**H**} & **Low** & **Medium** & **High** & **Low Channel** & **Medium Channel** & **High Channel** & **Critical** \\  & & **Channel** & **Channel** & **Channel** & **Statistical Test** & **Statistical Test** & **Statistical Test** & **Value** \\ \hline
10 & 0 & 0.424 & 0.402 & 0.701 & 25,787 & 26,701 & 33,455 & 18.3 \\
15 & 0 & 0.7014 & 0.6883 & 0.8236 & 26,447 & 28,617 & 37,143 & 24.99 \\
20 & 0 & 0.947 & 0.876 & 0.9355 & 26,945 & 30,313 & 40,772 & 31.41 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Ljung-Box-Pierce Q-Test in standardized innovations for GSM channels. CR BS. This provides a better processor than that of the CR user, and has no limitations on power consumption. However, there is a time period between data capture in the environment and the processing, which adds a delay to the response. This must not be ignored, but the forecast helps to reduce the negative impact of the delayed response. The analysis of the precision of the forecast made with the SARIMA and GARCH algorithms is presented, as follows. Figure 15 shows the SARIMA algorithm forecasts obtained from Equations (7)-(9), and from GARCH algorithm based on Equations (11)-(16). This was contrasted with the power measured data of Friday from 5:00 p.m. to 6:00 p.m. This period was chosen since during this time an increased use of the channels by PUs was perceived. In Figures 16 and 17, availability and occupancy times of the measured and forecast channels are presented. Availability time allows us to analyze the precision with which SUs could use availability time in GSM channels for a CR system. In the same way, occupancy time examines the precision during time in which PUs use GSM channels. Average precisions obtained between actual and forecast data for availability times were: 82%, 54% and 60%, for the SARIMA algorithm; and 31%, 30% and 43%, for the GARCH algorithm, corresponding to channels with low, medium and high occupation, respectively. Average precisions for occupation times between real data and forecast data are equivalent to 58%, 77% and 78% for the SARIMA algorithm; and 44%, 46.6% and 44.2%, for the GARCH algorithm,  
Figure 14: Example of application to forecast the received power from the base station (BS). CR: cognitive radio. Figure 15: GSM channel series and forecast series with SARIMA and GARCH algorithms. corresponding to channels with low, medium and high occupancy levels, respectively. Additionally, as expected, for each algorithm there is an inversely proportional relationship between channel occupancy and availability time, as well as a directly proportional relationship between occupancy probability and occupancy time of the channels. In Table 13 forecast and measured data are compared to different methods for error estimation such as SMAPE, MAPE and MAE. Results of Table 13 point that only in data forecast for the medium occupancy channel, the GARCH algorithm presents smaller errors than the SARIMA algorithm.