Limiting Distributions of Nonlinear Vector Functions of Stationary Gaussian Processes

Ho, Hwai‐Chung; Sun, Tze-Chien

doi:10.1214/aop/1176990740

Cited by 15 publications

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“…Observe that the same sequence ¹X n º is involved in each component of V N , in contrast to Ho and Sun (1990) who consider the case J D 2 and ¹.X n ; Y n /º is a bivariate Gaussian vector series. Note also that convergence in f.d.d.…”

Section: Introductionmentioning

confidence: 99%

“…(2) where G j , j D 1; : : : ; J , are nonlinear functions, t > 0 is the time variable and A j .N /'s are appropriate normalizations that make the variance of each component at t D 1 tend to 1. Observe that the same sequence ¹X n º is involved in each component of V N , in contrast to Ho and Sun (1990) who consider the case J D 2 and ¹.X n ; Y n /º is a bivariate Gaussian vector series. Note also that convergence in f.d.d.…”

Section: Introductionmentioning

confidence: 99%

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Multivariate Limit Theorems in the Context of Long‐range Dependence

Taqqu

Bai

2013

Journal Time Series Analysis

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We study the limit law of a vector made up of normalized sums of functions of long-range dependent stationary Gaussian series. Depending on the memory parameter of the Gaussian series and on the Hermite ranks of the functions, the resulting limit law may be (a) a multi-variate Gaussian process involving dependent Brownian motion marginals, (b) a multi-variate process involving dependent Hermite processes as marginals or (c) a combination. We treat cases (a) and (b) in general and case (c) when the Hermite components involve ranks 1 and 2. We include a conjecture about case (c) when the Hermite ranks are arbitrary, although the conjecture can be resolved in some special cases.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%