# Anomaly Detection in IoT Communication Network Based on Spectral Analysis and Hurst Exponent
## 5 Results
### Network Traffic Stationery and Spectrum Analysis--General Information  
The proposed process of anomaly detection by comparing multifractal spectra following the presented concept must be preceded by the verification of the character of the traffic, i.e., its stationary character. The values of standard deviations differ depending on the sample and the average length of the data packets of the sets. In the case of the 2016 samples, the changes in the deviations were small. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & \multicolumn{2}{c}{**21.01.2016**} & \multicolumn{2}{c}{**18.02.2016**} & \multicolumn{2}{c}{**17.03.2016**} & \multicolumn{2}{c}{**06.04.2016**} \\ \cline{3-10}  & & & \begin{tabular}{c} Data \\ sample \\ \end{tabular} & \begin{tabular}{c} Total \\ traffic \\ \end{tabular} & \begin{tabular}{c} Data \\ sample \\ \end{tabular} & \begin{tabular}{c} Total \\ traffic \\ \end{tabular} & \begin{tabular}{c} Data \\ sample \\ \end{tabular} & \begin{tabular}{c} Total \\ traffic \\ \end{tabular} & \begin{tabular}{c} Data \\ sample \\ \end{tabular} & \
\begin{tabular}{c} Total \\ traffic \\ \end{tabular} \\ \hline \multirow{6}{*}{**Category**} & \multirow{2}{*}{
\begin{tabular}{c} Packets \\ Sum (B) \\ Average packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ Variance packet size (B) \\ \\ \hline \end{tabular}
\end{table} 
Table 1: Aggregate summary of all network traffic samples undergoing long-term and multifractal analysis. This means that for the data in sample B for 2016 with the higher average packet lengths, the standard deviation (defining the scattering of values around the mean) was lower compared to those in sample A. On the other hand, the standard deviations of the 2018 data samples was proportionally varied to the average size of the data packet. Minor differences could be observed, especially for data samples A and B of 2018. For these sets, the discrepancy between the compared results was significant. In the case of variance, the values for each sample were distributed in a similar way to the results of the standard deviations. The analysis of network traffic samples from 2016 and 2018 consisted of determining the estimated values of Hurst's exponent and setting different intervals dividing the data into sub-series. The size of these intervals was selected within the range of multiples of number 2 from 21 to 211. Based on the results of estimates using the OriginPro 2017 tool, a graph of the [PERSON]'s exponent distribution was generated for each tested network traffic sample. The estimation of [PERSON]'s exponent value for network traffic samples consisted of the 30 thousand records allowed for the evaluation of the characteristics of the given traffic sample. On the strength of the data, an upward trend in the calculated exponent values could be observed. The phenomenon presented above may have been caused by the characteristics of network traffic changes over time. The development of the IoT caused an increase in the number of new devices generating network traffic, which had an impact on the changing characteristics of packet flow in the network. Only one average estimated value reached a level below 0.7. The difference between the extreme values was approximately 0.09.