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| Main Authors: | , |
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| Format: | Preprint |
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2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2111.07650 |
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| _version_ | 1866909395849314304 |
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| author | Bräutigam, Marcel Kratz, Marie |
| author_facet | Bräutigam, Marcel Kratz, Marie |
| contents | In this paper, we establish a joint (bivariate) functional central limit theorem of the sample quantile and the $r$-th absolute centred sample moment for functionals of mixing processes. More precisely, we consider $L_2$-near epoch dependent processes that are functionals of either $ϕ$-mixing or absolutely regular processes. The general results we obtain can be used for two classes of popular and important processes in applications: The class of augmented GARCH($p$,$q$) processes with independent and identically distributed innovations (including many GARCH variations used in practice) and the class of ARMA($p$,$q$) processes with mixing innovations (including, e.g., ARMA-GARCH processes). For selected examples, we provide exact conditions on the moments and parameters of the process for the joint asymptotics to hold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_07650 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Joint FCLT for Sample Quantile and Measures of Dispersion for Functionals of Mixing Processes Bräutigam, Marcel Kratz, Marie Statistics Theory 60F05, 60F17, 60G10, 62H10, 62H20 In this paper, we establish a joint (bivariate) functional central limit theorem of the sample quantile and the $r$-th absolute centred sample moment for functionals of mixing processes. More precisely, we consider $L_2$-near epoch dependent processes that are functionals of either $ϕ$-mixing or absolutely regular processes. The general results we obtain can be used for two classes of popular and important processes in applications: The class of augmented GARCH($p$,$q$) processes with independent and identically distributed innovations (including many GARCH variations used in practice) and the class of ARMA($p$,$q$) processes with mixing innovations (including, e.g., ARMA-GARCH processes). For selected examples, we provide exact conditions on the moments and parameters of the process for the joint asymptotics to hold. |
| title | Joint FCLT for Sample Quantile and Measures of Dispersion for Functionals of Mixing Processes |
| topic | Statistics Theory 60F05, 60F17, 60G10, 62H10, 62H20 |
| url | https://arxiv.org/abs/2111.07650 |