Asymptotic Inference in Multiple-Threshold Nonlinear Time Series Models

Dong Li (), Shiqing Ling () and Jean-Michel Zakoian
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Dong Li: Tsinghua University

No 2013-51, Working Papers from Center for Research in Economics and Statistics

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 U.S. 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)
Pages: 27
Date: 2013-12
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