This work deals with a sample of probability density functions calculated from a time series of high frequency Bitcoins returns. Taking advantage on the functional nature of these data, a study of the complexity, a concept tied to the minimum number of random sources used to define the underlying process, is performed. In particular a mixture of processes with different complexities is identified and studied through the use of the small-ball probability of the process. Based on a theoretical discussion about the complexity mixture process structure, a heuristic method is proposed to isolate the different components of the mixture.

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Analysing the Complexity Mixture Structure of Daily Probability Densities of Bitcoin Returns

  • Enea G. Bongiorno,
  • Lax Chan,
  • Aldo Goia

摘要

This work deals with a sample of probability density functions calculated from a time series of high frequency Bitcoins returns. Taking advantage on the functional nature of these data, a study of the complexity, a concept tied to the minimum number of random sources used to define the underlying process, is performed. In particular a mixture of processes with different complexities is identified and studied through the use of the small-ball probability of the process. Based on a theoretical discussion about the complexity mixture process structure, a heuristic method is proposed to isolate the different components of the mixture.