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Bootstrap for integer‐valued GARCH( p ,  q ) processes
Author(s) -
Neumann Michael H.
Publication year - 2021
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/stan.12238
Subject(s) - mathematics , autoregressive model , heteroscedasticity , autoregressive conditional heteroskedasticity , contraction (grammar) , kernel (algebra) , uniqueness , discrete mathematics , statistics , econometrics , mathematical analysis , volatility (finance) , medicine
We consider integer‐valued processes with a linear or nonlinear generalized autoregressive conditional heteroscedastic models structure, where the count variables given the past follow a Poisson distribution. We show that a contraction condition imposed on the intensity function yields a contraction property of the Markov kernel of the process. This allows almost effortless proofs of the existence and uniqueness of a stationary distribution as well as of absolute regularity of the count process. As our main result, we construct a coupling of the original process and a model‐based bootstrap counterpart. Using a contraction property of the Markov kernel of the coupled process we obtain bootstrap consistency for different types of statistics.

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