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Asymptotic Inference in Multiple-Threshold Nonlinear Time Series Models

Author

Listed:
  • Dong Li

    () (Tsinghua University)

  • Shiqing Ling

    () (Hong kong University of Science and Technology)

  • Jean-Michel Zakoian

    () (CREST)

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

Suggested Citation

  • Dong Li & Shiqing Ling & Jean-Michel Zakoian, 2013. "Asymptotic Inference in Multiple-Threshold Nonlinear Time Series Models," Working Papers 2013-51, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2013-51
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Compound Poisson process; Ergodicity; Quasi-maximum likelihood estimation; Strict stationarity; MTDAR model; Score test;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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