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.

Issue Section:
Technical Briefs
Keywords:
ARMA model, fractal dimension, multiple regression analysis
Topics:
Dimensions, Fractals, Regression analysis
1.
Pandit, S. M., and Wu, S. M., 1983, Time Series and System Analysis with Applications, John Wiley and Sons, pp. 13–44.
2.
Hasegawa
M.
,
Liu
J. C.
, and
Konishi
Y.
,
1993
, “
Characterization of Engineering Surface by Fractal Analysis
,”
Int. J. of Japan Soc. for Pre. Eng.
, Vol.
27
, pp.
192
–
197
.
3.
Majumdar
A.
, and
Bhushan
B.
,
1990
, “
Role of Fractal Geometry in Roughness Characterization and Contact Mechanics of Surface Roughness
,”
ASME Journal of Tribology
, Vol.
112
, pp.
205
–
215
.
4.
Hasegawa, M., Liu, J. C., Okuda, K., and Nunobiki, M., 1994, “Fractal Dimension of Machined Surface Texture,” Proceedings of ICPG94, N. Norihiko et al., ed., International Academic Publisher, pp. 727–733.
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