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WHY FARIMA MODELS ARE BRITTLE

D. VEITCH

Department of Electrical and Electronic Engineering, The University of Melbourne, Victoria 3010, Australia

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A. GORST-RASMUSSEN

Department of Electrical and Electronic Engineering, The University of Melbourne, Victoria 3010, Australia

Current affiliation: Department of Mathematical Sciences, Aalborg University, 9220 Aalborg East, Denmark

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A. GEFFERTH

Department of Electrical and Electronic Engineering, The University of Melbourne, Victoria 3010, Australia

Current affiliation: Innovació i Recerca Industrial i Sostenible, Avda. Carl Friedrich Gauss n11, 08860 Castelldefels, Spain

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https://doi.org/10.1142/S0218348X13500126Cited by:5 (Source: Crossref)

Abstract

The FARIMA models, which have long-range-dependence (LRD), are widely used in many areas. Through the derivation of a precise characterization of the spectrum and variance time function, we show that this family is very atypical among LRD processes, being extremely close to the fractional Gaussian noise in a precise sense which results in ultra-fast convergence to fGn under rescaling. Furthermore, we show that this closeness property is not robust to additive noise. We argue that the use of FARIMA, and more generally fractionally differenced time series, should be reassessed in some contexts, in particular when convergence rate under rescaling is important and noise is expected.

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