Proper ARMA Modeling and Forecasting in the Generalized Segre’s Quaternions Domain

The analysis of time series in 4D commutative hypercomplex algebras is introduced. Firstly, generalized Segre’s quaternion (GSQ) random variables and signals are studied. Then, two concepts properness suggested statistical tests to check if a GSQ vector proper or not proposed. Further, method determine which specific algebra most likely achieve, possible, the properties given. Next, both linear estimation prediction problems studied domain. Finally, ARMA modeling forecasting for tackled. Experimental results show superiority proposed approach over its counterpart Hamilton