[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14317/jami.2015.203

PARAMETER ESTIMATION AND SPECTRUM OF FRACTIONAL ARIMA PROCESS

Kim, Joo-Mok (School of General Education, Semyung University)
Kim, Yun-Kyong (Department of Information and Communication Engineering, Donghin University)

Publication Information

Journal of applied mathematics & informatics / v.33, no.1_2, 2015 , pp. 203-210 More about this Journal

Abstract

We consider fractional Brownian motion and FARIMA process with Gaussian innovations and show that the suitably scaled distributions of the FARIMA processes converge to fractional Brownian motion in the sense of finite dimensional distributions. We figure out ACF function and estimate the self-similarity parameter H of FARIMA(0, d, 0) by using R/S method. Finally, we display power spectrum density of FARIMA process.

Keywords

Self-Similar; FARIMA; FBM; R/S method; Power Spectrum Density;

Citations & Related Records

Reference

1	N.G. Duffield and N. O'Connell, Large daviations and overflow probabilities for the general single-server queue with applications, Math. Proc. Com. Phil. Soc., 118 (1995), 363-374. DOI
2	M. Garrett and W. Willinger. Analysis, modeling and generation of self similar vbr video traffic, in Proceedings SIGCOMM'94, 269-280, August 1994.
3	N. Laskin, I. Lambadaris, F. Harmantzis and M. Devetsikiotis, Fractional Levy Motions and its application to Network Traffic Modeling, Submitted.
4	J.C. Lopez-Ardao, P. Argibay-Losada and R.F. Rodriguez-Rubio, On Modeling MPEG Vido at the Frame Level Using Self-similar Processes, MIPS 2004, 37-48, 2004.
5	P. Rabinovitch, Statistical estimation of effective bandwidth, Information and System Sciences, 2000.
6	G. Samorodnitsky and M. S. Taqqu, Stable non-Gaussian processes: Stochastic models with Infinite Variance, Chapman and Hall, New York, London, 1994.
7	O.I. Sheluhin, S.M. Smolskiy and A.V. Osin, Self-Similar Processes in Telecomunications, J.Wiley and Sons, 2007.
8	B. Sikdar and K.S. Vastola, On the Convergence of MMPP and Fractional ARIMA processes with long-range dependence to Fractional Brownian motion, Proc. of the 34th CISS, Prinston, NJ, 2000.
9	H.Stark and J.W.Woods, Probability and Random Processes with Applications to Signal Processing, Prince Hall, 2002.
10	X. Tan, Z. Tan and W. Fang, Study of Network Traffic Analysis Model, The 2013 AASRI Winter International Conference On Engineering and Technology.
11	M. S. Taqqu and V. Teverovsky, Robustness of Whittle-type estimators for time series with long-range dependence, Stochastic Models, 13(1997), 723-757. DOI ScienceOn
12	M. S. Taqqu and V. Teverovsky, On Estimating the intensity of long-range dependence in finite and infinte variance time series, A practical guide to heavy tails : Statistical Techniques for Analyzing heavy tailed distributions, Birkhauser, Boston, 1996.
13	M. S. Taqqu, V. Teverovsky and W. Willinger, Estimators for long-range dependence : Empirical study, Fractals, 3(1995), 785-798. DOI
14	M. S. Taqqu, W. Willinger and R. Sherman, Proof of a fundamental result in self-similar traffic modeling, Computer Communication review, 27(1997), 5-23.