Long-range dependence is being identified many disciplines such as, networking, databases, economics, climate and biodiversity. LTP is competing with the sexy “long tail” for top spot as a theory of cultural consumption. Thus, the need for software offering complete long-range dependence analysis is crucial.
While there are some steps towards this direction, none are yet completely satisfactory. For one, the Hurst exponent cannot be calculated in a definitive way, it can only be estimated. Second, there are several different methods to estimate the Hurst exponent, but they often produce conflicting estimates, and it is not clear which of the estimators are most accurate.
A first step towards a systematic approach in estimating self-similarity and long-range dependence is the java tool called SELFIS, a java based tool that will automate the self-similarity analysis.
In R there is the fracdiff package on CRAN for fitting
frARIMA(p,d,q) models with fractional “d” and there’s a
one-to-one relationship between ‘d’ and the Hurst parameter for
these models: d = H – 1/2. These are better than the R/S method known to be far from optimal.
A useful summary of the issues and reference to other resources is
Estimating the Hurst Exponent.
Demonstrating just how pervasive are these concepts in our daily life is the Physics of Fashion Fluctuations by
R. Donangeloa, A. Hansenb,c, K. Sneppenb and S. R. Souzaa.
Here a simple model for emergence of fashions â€” goods that become popular not due to any intrinsic value, but simply because â€œeverybody wants itâ€ â€” in markets where people trade goods shows spontaneous emergence of random products as money. The model supports collectively driven fluctuations characterized by a Hurst exponent of about 0.7.
Scale Invariance for Dummies is an investigation of scale invariance or long term persistence (LTP) in time series including tree-ring proxies â€“ the recognition, quantification and implications for analysis â€“ drawn largely from Koutsoyiannis.
Anybody know of any commercial packages dealing with the Hurst coefficient?