# Time Series Analysis to Predict End-to-End Quality of Wireless Community Networks +
## 4 Time-Series Analysis to Predict EtEQ
### EtEQ Prediction with Rule-Based Regression  
We proceeded next to analyze more in depth the EtEQ using the RBR algorithm to discover how can we reach a satisfactory level of one-step prediction.  
Figure 11 presents box plots of the MAE of path ETX prediction with RBR, versus the number of Hops corresponding to the paths. We used the same training dataset as Section 4.2. Even though the dispersion of the error seems high in specific cases (for example 10, 11, and 13 hops), the results follow the dispersion pattern of actual ETX values as described in Figure 7, although at a much smaller scale. In other words, even though ETX values for 10, 11, and 13 hop paths have a high dispersion, our prediction manages to successfully predict a big percentage of the fluctuations. For instance, the dispersion of 13 hop path-ETX is 6, while the error of its prediction has a maximum value of 3.  
Figure 12 presents another point of view of the RBR Mean Absolute Error (MAE) to clarify how the mean quality of the path influences the performance of the algorithm. This histogram shows that more than 90% of predictions has a MAE lower than 0.5, almost without error. Moreover, this corresponds to paths with a few hops. The remaining 10%, which presents bigger errors, are associated to paths with many hops (as can be seen in Figure 11).  
Figure 11: Distribution of the RBR Mean Absolute Error (MAE) as box plot.  
Figure 10: Mean Absolute Error (MAE) of the EtEQ predictions as box plot.  
Figure 13 provides a more detailed analysis of the prediction accuracy. We can see that the average ETX value and the average prediction value are very close, even overlapping during the first half of prediction test. A better estimation for the deviation of the individual path values is given by the average absolute-error line. Notice that the deviation remains less than 0.5 throughout the whole prediction, which is a great achievement. Nevertheless, the potential impact of this small error in routing decisions can be further studied.  
Another characteristic of the prediction revealed by Figure 13 is that after 100 steps of prediction (between 08:00 and 08:30) the absolute error presents an increasing trend. We assume that this outcome is an effect of the actual ETX oscillations depicted in Figure 4. To verify this assumption, we performed two more prediction tests. From 00:00 to 12:00 (Figure 14.top) and from 12:00 to 00:00 (Figure 14.bottom), using as training dataset the 2160 more recent instances (7.5 days before prediction starts), a test dataset of 144 instances (half a day), and a lag window composed of the last 12. With these changes in the training configuration (7.5 + 0.5 days), the results obtained are almost identical to the results of Figure 13 (with 7 + 1 days), leading us to conclude that ETX oscillations (higher between 12:00 to 00:00) are indeed influencing the prediction. This led us to consider different predictors for day and night to increase predictor accuracy.  
Figure 14: Evolution of the average ETX, the average prediction and the average absolute error for: (**top**) 12:00–00:00 and (**bottom**) 00:00–12:00.  
Figure 13: Evolution of the average ETX, the average prediction and the average absolute error.