A functional limit theorem for η-weakly dependent processes and its applications

Jean Marc Bardet; Paul Doukhan; José Rafael León

doi:10.1007/s11203-007-9015-y

A functional limit theorem for η-weakly dependent processes and its applications

Jean Marc Bardet
, Paul Doukhan
, José Rafael León

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a general functional central limit theorem for weak dependent time series. A very large variety of models, for instance, causal or non causal linear, ARCH(∞), LARCH(∞), Volterra processes, satisfies this theorem. Moreover, it provides numerous applications as well for bounding the distance between the empirical mean and the Gaussian measure than for obtaining central limit theorem for sample moments and cumulants.

Original language	English
Pages (from-to)	265-280
Number of pages	16
Journal	Statistical Inference for Stochastic Processes
Volume	11
Issue number	3
DOIs	https://doi.org/10.1007/s11203-007-9015-y
Publication status	Published - 1 Oct 2008
Externally published	Yes

Keywords

Central limit theorem
Sample moments and cumulants
Weakly dependent processes

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10.1007/s11203-007-9015-y

Cite this

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abstract = "We prove a general functional central limit theorem for weak dependent time series. A very large variety of models, for instance, causal or non causal linear, ARCH(∞), LARCH(∞), Volterra processes, satisfies this theorem. Moreover, it provides numerous applications as well for bounding the distance between the empirical mean and the Gaussian measure than for obtaining central limit theorem for sample moments and cumulants.",

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AU - León, José Rafael

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N2 - We prove a general functional central limit theorem for weak dependent time series. A very large variety of models, for instance, causal or non causal linear, ARCH(∞), LARCH(∞), Volterra processes, satisfies this theorem. Moreover, it provides numerous applications as well for bounding the distance between the empirical mean and the Gaussian measure than for obtaining central limit theorem for sample moments and cumulants.

AB - We prove a general functional central limit theorem for weak dependent time series. A very large variety of models, for instance, causal or non causal linear, ARCH(∞), LARCH(∞), Volterra processes, satisfies this theorem. Moreover, it provides numerous applications as well for bounding the distance between the empirical mean and the Gaussian measure than for obtaining central limit theorem for sample moments and cumulants.

KW - Central limit theorem

KW - Sample moments and cumulants

KW - Weakly dependent processes

UR - https://www.scopus.com/pages/publications/51649129594

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DO - 10.1007/s11203-007-9015-y

M3 - Article

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EP - 280

JO - Statistical Inference for Stochastic Processes

JF - Statistical Inference for Stochastic Processes

IS - 3

ER -

A functional limit theorem for η-weakly dependent processes and its applications

Abstract

Keywords

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