Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/305435 
Year of Publication: 
2023
Citation: 
[Journal:] Metrika [ISSN:] 1435-926X [Volume:] 87 [Issue:] 1 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2023 [Pages:] 31-59
Publisher: 
Springer, Berlin, Heidelberg
Abstract: 
The Markov property is shared by several popular models for time series such as autoregressive or integer-valued autoregressive processes as well as integer-valued ARCH processes. A natural assumption which is fulfilled by corresponding parametric versions of these models is that the random variable at time  t gets stochastically greater conditioned on the past, as the value of the random variable at time  t-1increases. Then the associated family of conditional distribution functions has a certain monotonicity property which allows us to employ a nonparametric antitonic estimator. This estimator does not involve any tuning parameter which controls the degree of smoothing and is therefore easy to apply. Nevertheless, it is shown that it attains a rate of convergence which is known to be optimal in similar cases. This estimator forms the basis for a new method of bootstrapping Markov chains which inherits the properties of simplicity and consistency from the underlying estimator of the conditional distribution function.
Subjects: 
Autoregressive process
Bootstrap
INAR
Integer-valued ARCH
Markov chain
Stochastic order
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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