Tsallis Entropy Perspective on Multivariate Controlled Autoregressive Fractional Integrated Moving Average System

Abstract

In this study, we have investigated Tsallis entropy of a multivariate controlled autoregressive fractional integrated moving average (MCARFIMA) system. A characteristic function of this system state is derived using the corresponding its residual characteristic functions.

Furthermore, an analytical expression for the Tsallis entropy of system process is established under independent condition between the control process and moving average. An algorithm is proposed to calculate the values of Tsallis entropy of system process when it is influenced by Gaussian and Cauchy processes.  The results are discussed and analyzed to demonstrate the fractional integrated on the system’s informational structure and dynamical behaviour.  Finally, an example is given to illustrative the proposed algorithm and information behaviour of proposed system under Gaussian process.