Estimation and bootstrap for stochastically monotone Markov processes

Michael H. Neumann ()
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Michael H. Neumann: Friedrich-Schiller-Universität Jena

Metrika: International Journal for Theoretical and Applied Statistics, 2024, vol. 87, issue 1, No 3, 59 pages

Abstract: 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 $$t-1$$ t - 1 increases. 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.

Keywords: Autoregressive process; Bootstrap; INAR; Integer-valued ARCH; Markov chain; Stochastic order; Primary 60G10; Secondary 60J05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00184-023-00903-7

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