Estimation of seasonal long-memory parameters

Alomari, Huda Mohammed; Ayache, Antoine; Fradon, Myriam; Olenko, Andriy

doi:10.48550/arxiv.1805.11905

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2019

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“…Linear stochastic processes and random fields obtained as outputs of filters are popular models in various applications, see [3,17,18,41]. In engineering practice it is often assumed that a narrow band-pass filter applied to a stationary random input yields an approximately normally distributed output.…”

Section: Introductionmentioning

confidence: 99%

Limit theorems for filtered long-range dependent random fields

2019

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This article investigates general scaling settings and limit distributions of functionals of filtered random fields. The filters are defined by the convolution of non-random kernels with functions of Gaussian random fields. The case of long-range dependent fields and increasing observation windows is studied. The obtained limit random processes are non-Gaussian. Most known results on this topic give asymptotic processes that always exhibit non-negative auto-correlation structures and have the self-similar parameter H ∈ ( 1 2 , 1). In this work we also obtain convergence for the case H ∈ (0, 1 2 ) and show how the Hurst parameter H can depend on the shape of the observation windows. Various examples are presented.Keywords filtered random fields · long-range dependence · self-similar processes · non-central limit theorem · Hurst parameter Mathematics Subject Classification (2010) 60G60 · 60F17 · 60F05 · 60G35

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Section: Introductionmentioning

confidence: 99%