Quadratic sample entropy as a measure of burstiness : A study in how well Rényi entropy rate and quadratic sampleentropy can capture the presence of spikes in time-series data

Abstract: Requests to internet servers do not in general behave in a manner which can be easily modelled and forecast with typical time-series methods, but often have a significant presence of spikes in the data, a property we call “burstiness”. In this thesis we study various entropy measures and their properties for different distributions, both theoretically and via simulation, in order to better find out how these measures could be used to characterise the predictability and burstiness of time series. We find that a low entropy can indicate a heavy-tailed distribution, which for time series corresponds to a high burstiness. Using a previous result that connects the quadratic sample entropy for a time series with the Rényi entropy rate of order 2, we suggest a way of detecting burstiness by comparing the quadratic sample entropy of the time series with the Rényi entropy rate of order 2 for a symmetric and a heavy-tailed distribution.