A Study on Fractal Characteristics of ARMA Model

[+] Author and Article Information
M. Hasegawa, J. C. Liu, K. Okuda, M. Nunobiki

Department of Mechanical and Intelligent Engineering, Himeji Institute of Technology, Shosha 2167, Himeji, Japan

J. Manuf. Sci. Eng 118(4), 677-680 (Nov 01, 1996) (4 pages) doi:10.1115/1.2831087 History: Received July 01, 1994; Revised September 01, 1995; Online January 17, 2008


This paper discusses the fractal characteristics of the autoregressive moving average (ARMA) model, which has been considered as one of the useful approaches for investigating the random engineering phenomena. Firstly, the fractal characteristic of the ARMA model is proven using the variation method. Then, based on this result, the relationships between the fractal dimensions of the AR (1), the AR (2) and the ARMA (2,1) models and autoregressive and moving average parameters of these models are illustrated quantitatively by using the multiple regression analysis.

Copyright © 1996 by The American Society of Mechanical Engineers
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