Entropy Analysis of Multivariate Fractional Controlled ARMA Systems

Abstract

In this paper, entropy measure is used as effective tool to analysis the behavior of controlled autoregressive moving average system of fractional order (FCARMA). The characteristic function technique is employed of output state, through it, entropy is computed in its three types Shannon, Rényi and Tsallis. The important aspect of this work is that we consider and discuss the controlled ARMA System when it is affected by fractional order for the entire system, not just for a specific part as in ARIMA. Additionally, we introduce an algorithm to calculate the values of entropy when it is influenced by Gaussian and Cauchy processes. Finally, examples are given to illustrative the information behavior and proposed algorithm of system under Gaussian process and Cauchy processes.