Testing in GARCH-X Type Models

Rasmus Søndergaard Pedersen; Anders Rahbek

doi:10.1017/S026646661800035X

Testing in GARCH-X Type Models

Rasmus Søndergaard Pedersen, Anders Rahbek

8 Citationer (Scopus)

Abstract

We present novel theory for testing for reduction of GARCH-X type models with an exogenous (X) covariate to standard GARCH type models. To deal with the problems of potential nuisance parameters on the boundary of the parameter space as well as lack of identification under the null, we exploit a noticeable property of specific zero-entries in the inverse information of the GARCH-X type models. Specifically, we consider sequential testing based on two likelihood ratio tests and as demonstrated the structure of the inverse information implies that the proposed test neither depends on whether the nuisance parameters lie on the boundary of the parameter space, nor on lack of identification. Asymptotic theory is derived essentially under stationarity and ergodicity, coupled with a regularity assumption on the exogenous covariate X. Our general results on GARCH-X type models are applied to Gaussian based GARCH-X models, GARCH-X models with Student’s t-distributed innovations as well as integer-valued GARCH-X (PAR-X) models.

Originalsprog	Engelsk
Tidsskrift	Econometric Theory
Vol/bind	35
Udgave nummer	5
Sider (fra-til)	1012-1047
ISSN	0266-4666
DOI	https://doi.org/10.1017/S026646661800035X
Status	Udgivet - 2019

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10.1017/S026646661800035X

Citationsformater

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title = "Testing in GARCH-X Type Models",

abstract = "We present novel theory for testing for reduction of GARCH-X type models with an exogenous (X) covariate to standard GARCH type models. To deal with the problems of potential nuisance parameters on the boundary of the parameter space as well as lack of identification under the null, we exploit a noticeable property of specific zero-entries in the inverse information of the GARCH-X type models. Specifically, we consider sequential testing based on two likelihood ratio tests and as demonstrated the structure of the inverse information implies that the proposed test neither depends on whether the nuisance parameters lie on the boundary of the parameter space, nor on lack of identification. Asymptotic theory is derived essentially under stationarity and ergodicity, coupled with a regularity assumption on the exogenous covariate X. Our general results on GARCH-X type models are applied to Gaussian based GARCH-X models, GARCH-X models with Student{\textquoteright}s t-distributed innovations as well as integer-valued GARCH-X (PAR-X) models.",

author = "Pedersen, {Rasmus S{\o}ndergaard} and Anders Rahbek",

year = "2019",

doi = "10.1017/S026646661800035X",

language = "English",

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T1 - Testing in GARCH-X Type Models

AU - Pedersen, Rasmus Søndergaard

AU - Rahbek, Anders

PY - 2019

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N2 - We present novel theory for testing for reduction of GARCH-X type models with an exogenous (X) covariate to standard GARCH type models. To deal with the problems of potential nuisance parameters on the boundary of the parameter space as well as lack of identification under the null, we exploit a noticeable property of specific zero-entries in the inverse information of the GARCH-X type models. Specifically, we consider sequential testing based on two likelihood ratio tests and as demonstrated the structure of the inverse information implies that the proposed test neither depends on whether the nuisance parameters lie on the boundary of the parameter space, nor on lack of identification. Asymptotic theory is derived essentially under stationarity and ergodicity, coupled with a regularity assumption on the exogenous covariate X. Our general results on GARCH-X type models are applied to Gaussian based GARCH-X models, GARCH-X models with Student’s t-distributed innovations as well as integer-valued GARCH-X (PAR-X) models.

AB - We present novel theory for testing for reduction of GARCH-X type models with an exogenous (X) covariate to standard GARCH type models. To deal with the problems of potential nuisance parameters on the boundary of the parameter space as well as lack of identification under the null, we exploit a noticeable property of specific zero-entries in the inverse information of the GARCH-X type models. Specifically, we consider sequential testing based on two likelihood ratio tests and as demonstrated the structure of the inverse information implies that the proposed test neither depends on whether the nuisance parameters lie on the boundary of the parameter space, nor on lack of identification. Asymptotic theory is derived essentially under stationarity and ergodicity, coupled with a regularity assumption on the exogenous covariate X. Our general results on GARCH-X type models are applied to Gaussian based GARCH-X models, GARCH-X models with Student’s t-distributed innovations as well as integer-valued GARCH-X (PAR-X) models.

U2 - 10.1017/S026646661800035X

DO - 10.1017/S026646661800035X

M3 - Journal article

SN - 0266-4666

VL - 35

SP - 1012

EP - 1047

JO - Econometric Theory

JF - Econometric Theory

IS - 5

ER -

Testing in GARCH-X Type Models

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