Asymptotic inference in multiple-threshold double autoregressive models

Dong Li, Shiqing Ling and Jean-Michel Zakoian

Journal of Econometrics, 2015, vol. 189, issue 2, 415-427

Abstract: This paper investigates a class of multiple-threshold models, called Multiple Threshold Double AR (MTDAR) models. A sufficient condition is obtained for the existence and uniqueness of a strictly stationary and ergodic solution to the first-order MTDAR model. We study the Quasi-Maximum Likelihood Estimator (QMLE) of the MTDAR model. The estimated thresholds are shown to be n-consistent, asymptotically independent, and to converge weakly to the smallest minimizer of a two-sided compound Poisson process. The remaining parameters are n-consistent and asymptotically multivariate normal. In particular, these results apply to the multiple threshold ARCH model, with or without AR part, and to the multiple threshold AR models with ARCH errors. A score-based test is also presented to determine the number of thresholds in MTDAR models. The limiting distribution is shown to be distribution-free and is easy to implement in practice. Simulation studies are conducted to assess the performance of the QMLE and our score-based test in finite samples. The results are illustrated with an application to the quarterly US real GNP data over the period 1947–2013.

Keywords: Compound Poisson process; Ergodicity; Quasi-maximum likelihood estimation; Strict stationarity; MTDAR model; Score test (search for similar items in EconPapers)
JEL-codes: C13 C22 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:189:y:2015:i:2:p:415-427

DOI: 10.1016/j.jeconom.2015.03.033

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