## Abstract

Autoregressive processes (AR) have typical short-range memory. Detrended Fluctuation Analysis (DFA) was basically designed to reveal long-range correlations in non stationary processes. However DFA can also be regarded as a suitable method to investigate both long-range and short-range correlations in non stationary and stationary systems. Applying DFA to AR processes can help understanding the non-uniform correlation structure of such processes. We systematically investigated a first order autoregressive model AR(1) by DFA and established the relationship between the interaction constant of AR(1) and the DFA correlation exponent. The higher the interaction constant the higher is the short-range correlation exponent. They are exponentially related. The investigation was extended to AR(2) processes. The presence of an interaction between distant terms with characteristic time constant in the series, in addition to a near by interaction will increase the correlation exponent and the range of correlation while the effect of a distant negative interaction will significantly decrease the range of interaction, only. This analysis demonstrate the possibility to identify an AR(1) model in an unknown DFA plot or to distinguish between AR(1) and AR(2) models.

## Authors

V.V. **Morariu
**Department of Molecular and Biomolecular Physics, National Institute of R&D for Isotopic and Molecular Technology

L. **Buimaga-Iarinca
**Department of Molecular and Biomolecular Physics, National Institute of R&D for Isotopic and Molecular Technology

C. **Vamoș**

-Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

S.M. **Soltuz
**-Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

## Keywords

## Cite this paper as:

V.V. Morariu, L. Buimaga-Iarinca, C. Vamoş, Ş.M. Şoltuz, *Detrended fluctuation analysis of autoregressive processes*, Fluctuations and noise letters, Vol. 7, No. 3, 2007. pp. L249-L255, doi: 10.1142/S0219477507003908

### References

see the expansion block below.

Not available yet.

## About this paper

##### Journal

Fluctuations and noise letters

##### Publisher Name

World Scientific Publishing Company

##### Print ISSN

0219-4775

##### Online ISSN

1793-6780

## MR

?

## ZBL

?

- [1] W. Li, A Bibliography on 1/f Noise (1996-present), http://www.nslij-genetics.org/wli/1fnoise/[2] Wikipedia,
*Autoregressive moving average model*, http://en.wikipedia.org/wiki/

[3] P. J. Brockwell and R. A. Davies, Time Series: Theory and Methods, 2nd edn. (Springer, New York, 1991).

[4] F. N. Hooge, T. G. M. Kleinpenning, L. K. J. Vandamme, Experimental studies on 1/f noise, Rep. Progr. Phys. 44 (1981) 479–532.

[5] M.B. Weissman, 1/f noise and other slow, nonexponential kinetics in condensed matter, Rev. Mod. Phys. 60 (1988) 537–532.

[6] C.-K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley and A. L. Goldberger, Mosaic organization of DNA nucleotides, Phys. Rev. E 49 (1994) 1685–1689.

[7] K. Hu, P. Ch.Ivanov, Z. Chen, P. Carpena and H. Eugene Stanley, Effect of trends on detrended fluctuation analysis, Phys. Rev. E 64 (2001) 0111114–1.

[8] Z. Chen, P. Ch. Ivanov, K. Hu, H. Eugene Stanley, *Effect of nonstationarities on detrended fluctuation analysis*, Phys. Rev. E 65 (2002) 041107–1.

[9] A. Coza and V. V. Morariu, *Generating 1/f β noise with a low dimensional attractor characteristic: its significance for atomic vibrations in proteins and cognitive data,* Physica A 320 (2001) 449–460.

[10] M. König and J. Timmer, *Analyzing X-ray variability by linear state space model*, Astron. Astrophys. Suppl. Ser. 124 (1997) 589–596.

[11] Th. L. Thornton and D. L. Gilden, *Provenance of correlations in psychological data*, Psychonomic Bul. & Rev. 12 (2005) 409–441

soon