A weighted $$\chi ^2$$ χ 2 test to detect the presence of a major change point in non-stationary Markov chains

Alessandra Micheletti (), Giacomo Aletti, Giulia Ferrandi, Danilo Bertoni, Daniele Cavicchioli and Roberto Pretolani
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Alessandra Micheletti: Università degli Studi di Milano
Giacomo Aletti: Università degli Studi di Milano
Giulia Ferrandi: TU Eindhoven
Danilo Bertoni: Università degli Studi di Milano
Roberto Pretolani: Università degli Studi di Milano

Statistical Methods & Applications, 2020, vol. 29, issue 4, No 10, 899-912

Abstract: Abstract The problem of detecting a major change point in a stochastic process is often of interest in applications, in particular when the effects of modifications of some external variables, on the process itself, must be identified. We here propose a modification of the classical Pearson $$\chi ^2$$ χ 2 test to detect the presence of such major change point in the transition probabilities of an inhomogeneous discrete time Markov Chain, taking values in a finite space. The test can be applied also in presence of big identically distributed samples of the Markov Chain under study, which might not be necessarily independent. The test is based on the maximum likelihood estimate of the size of the ’right’ experimental unit, i.e. the units that must be aggregated to filter out the small scale variability of the transition probabilities. We here apply our test both to simulated data and to a real dataset, to study the impact, on farmland uses, of the new Common Agricultural Policy, which entered into force in EU in 2015.

Keywords: Weighted $$\chi ^2$$ χ 2 test; Inhomogeneous discrete time Markov chains; Nonparametric inference (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10260-020-00510-0

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