Statistical analysis of DWT coefficients of fGn processes using ARFIMA(p,d,q) models

Shivam Bhardwaj, Vikram M. Gadre and E. Chandrasekhar

Physica A: Statistical Mechanics and its Applications, 2020, vol. 547, issue C

Abstract: Fractional Gaussian noise (fGn) provides an important parametric representation for the data recorded from long-memory processes. Also it has been well established in literature that the orthogonal wavelet transforms prove to be the optimal bases to represent the data as fGn or fBm (fractional Brownian motion) models. This paper highlights the statistical properties of discrete wavelet transform (DWT) coefficients in the wavelet expansion of fGn. Statistical analysis was carried out by analyzing the inter-scale and intra-scale correlations of the DWT coefficients for wavelets with varying vanishing moments. Two types of auto-regressive moving average (ARMA) models were fit to the wavelet coefficients of fGn, namely, (i) ARMA(p,q) and (ii) ARFIMA(p,d,q) models. The latter represents the ARMA models with fractional differencing. Using the Akaike information criteria (AIC) and the Bayesian information criteria (BIC), it has been shown that ARFIMA models best represent the wavelet coefficients of fGn. The above observation holds good, when wavelets with increasing number of vanishing moments are used for obtaining DWT coefficients. After estimating the optimal model and its parameters, different properties pertaining to the inter-scale and intra-scale correlations were verified using these models.

Keywords: Discrete wavelet transform; Fractional Gaussian noise; ARFIMA(p,d,q) models; Akaike information criteria; Bayesian information criteria (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437120301564
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:547:y:2020:i:c:s0378437120301564

DOI: 10.1016/j.physa.2020.124404

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().