Testing in GARCH-X Type Models
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Testing in GARCH-X Type Models. / Pedersen, Rasmus Søndergaard; Rahbek, Anders.
I: Econometric Theory, Bind 35, Nr. 5, 2019, s. 1012-1047.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Testing in GARCH-X Type Models
AU - Pedersen, Rasmus Søndergaard
AU - Rahbek, Anders
PY - 2019
Y1 - 2019
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
VL - 35
SP - 1012
EP - 1047
JO - Econometric Theory
JF - Econometric Theory
SN - 0266-4666
IS - 5
ER -
ID: 200352389