Subgeometrically ergodic autoregressions

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Abstract

In this paper we discuss how the notion of subgeometric ergodicity in Markov chain theory can be exploited to study the stability of nonlinear time series models. Subgeometric ergodicity means that the transition probability measures converge to the stationary measure at a rate slower than geometric. Specifically, we consider higher-order nonlinear autoregressions that may exhibit rather arbitrary behavior for moderate values of the observed series and that behave in a near unit root manner for large values of the observed series. Generalizing existing first-order results, we show that these autoregressions are, under appropriate conditions, subgeometrically ergodic. As useful implications we also obtain stationarity and β-mixing with subgeometrically decaying mixing coefficients.
Original languageEnglish
Article numberarXiv:1904.07089
JournalarXiv.org
Number of pages34
ISSN2331-8422
Publication statusPublished - Apr 2019
MoE publication typeB1 Journal article

Fields of Science

  • 511 Economics
  • 112 Statistics and probability

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