Characterizations of the Moments of the Purely Diagonal Bilinear Time Series Model of Order One

by Ohakwe, Johnson and Iheanyi S. Iwueze.

Abstract: In this paper, we study the dissimilarities between a purely diagonal bilinear process of order one [PDB(1)] and a moving average process of order one [MA(1)] by comparing their first, second and fourth order moments. The well known similarity between their covariance structure was discovered to be true only when the autocorrelation function at lag one lies between zero and 0.16. With respect to the fourth moments, the PDB(1) process identifies as an autoregressive moving average process of order p=1 and q=1 while the equivalent non-zero mean MA(1) process identifies as an MA(1) process.

Key Words: Purely bilinear process, moving average process, moments, autocorrelation function, covariance structure

Authors:
Johnson Ohakwe, johakwe@yahoo.com
Iheanyi S. Iwueze, isiwueze@yahoo.com

Editor: Peiris Shelton, shelton@maths.usyd.edu.au

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