## 4 Analyses
### Discussion  
Most prominent variations in the statistical analysis are the minima and maxima of the signals, displayed by the whiskers in Figure 2. Mostly, maxima tend to decrease with the length of the aggregation period, meaning that longer aggregations smooth out peak values of the signal possibly annihilating anomalous conditions. If peak values are strongly reduced from the data, it can be assumed that also short negative spikes will undergo the same behavior. Except for the voltages, this cannot be seen in most plots as the minima coincide with those periods in which turbines are not operating. Still, this reduction of peak values might negatively impact the possible performance of early-fault detection algorithms and more general models attempting to represent the behavior of turbines under peak load conditions. For these use cases, high frequency SCADA should be considered.  
Mean and median values are almost constant with respect to the aggregation period length as the total weight of the values cannot be significantly shifted by averaging. The change of the standard deviation and the IQR behaves differently and can exhibit the following patterns: An increase means that several sudden outliers on short timescales are annihilated by the averaging process and, therefore, less data is distributed at the tails. A decrease is observed when the values move to the tails by the averaging process due to the majority of data inside an aggregation windows distributed at the tails.  
The shape indicators skewness and kurtosis do not provide completely conclusive information. However, there seems to be a connection between the reduction of the maximum or minimum and a decrease of the kurtosis, as can be seen for the wind speed, the generator speed, and the voltage. If due to the aggregation process there are less remote outliers, the probability distribution of the data becomes less spiked. Consequently, we can observe a loss of short-time peaks in the data by the reduction of the kurtosis. In contrast, the interpretation of the skewness is not as simple. However, it should give a hint to the direction of the majority of outliers or peaks, respectively. For the wind speed the skewness becomes less negative, telling us, that most of the outliers in the positive direction for the 1 s data will be smoothed out with increasing aggregation time. For the generator speed of the exemplary turbine in Figure 2 more outliers from the negative direction are smoothed. Please note again, that these are not generally valid as, except for the wind speed, the behavior of the skewness of a signal varies from turbine to turbine in the given dataset.  
Observing the behavior of a set of descriptive statistics provides a simple check on the effect of temporal aggregation. The proposed analysis attempts to capture various characteristics of the signal distribution, including its shape, dispersion, and central behavior. Overall, this observation of descriptive statistics does not answer the question on how much information is lost due to temporal aggregation. Changes in the range and standard deviation of the signals provide a general indication of the effects of temporal aggregation for a set of signals. Although pointing at the temporally critical signals, they fail to quantify precisely the loss of information. Moreover, this approach does not provide insights into the dynamic behavior of the signals as all indicators provide only a global perspective. Providing indications on the optimal frequency of a signal based on the value of descriptive statistics is particularly challenging.