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Inference for Heavy-Tailed and Multiple-Threshold Double Autoregressive Models

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  • Yaxing Yang
  • Shiqing Ling

Abstract

This article develops a systematic inference procedure for heavy-tailed and multiple-threshold double autoregressive (MTDAR) models. We first study its quasi-maximum exponential likelihood estimator (QMELE). It is shown that the estimated thresholds are n-consistent, each of which converges weakly to the smallest minimizer of a two-sided compound Poisson process. The remaining parameters are n$\sqrt{n}$-consistent and asymptotically normal. Based on this theory, a score-based test is developed to identify the number of thresholds in the model. Furthermore, we construct a mixed sign-based portmanteau test for model checking. Simulation study is carried out to access the performance of our procedure and a real example is given.

Suggested Citation

  • Yaxing Yang & Shiqing Ling, 2017. "Inference for Heavy-Tailed and Multiple-Threshold Double Autoregressive Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 318-333, April.
    • Handle: RePEc:taf:jnlbes:v:35:y:2017:i:2:p:318-333
    DOI: 10.1080/07350015.2015.1064433
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    References listed on IDEAS

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    1. Li, Dong & Ling, Shiqing, 2012. "On the least squares estimation of multiple-regime threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 167(1), pages 240-253.
    2. Zhu, Ke, 2012. "A mixed portmanteau test for ARMA-GARCH model by the quasi-maximum exponential likelihood estimation approach," MPRA Paper 40382, University Library of Munich, Germany.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Heung Wong & Shiqing Ling, 2005. "Mixed Portmanteau Tests for Time‐Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 569-579, July.
    5. Shiqing Ling & W. K. Li, 1997. "Diagnostic checking of nonlinear multivariate time series with multivariate arch errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(5), pages 447-464, September.
    6. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    7. Ngai Hang Chan & Liang Peng, 2005. "Weighted least absolute deviations estimation for an AR(1) process with ARCH(1) errors," Biometrika, Biometrika Trust, vol. 92(2), pages 477-484, June.
    8. Guodong Li & Wai Keung Li, 2005. "Diagnostic checking for time series models with conditional heteroscedasticity estimated by the least absolute deviation approach," Biometrika, Biometrika Trust, vol. 92(3), pages 691-701, September.
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    Cited by:

    1. Zhang, Xingfa & Zhang, Rongmao & Li, Yuan & Ling, Shiqing, 2022. "LADE-based inferences for autoregressive models with heavy-tailed G-GARCH(1, 1) noise," Journal of Econometrics, Elsevier, vol. 227(1), pages 228-240.
    2. Li, Dong & Tao, Yuxin & Yang, Yaxing & Zhang, Rongmao, 2023. "Maximum likelihood estimation for α-stable double autoregressive models," Journal of Econometrics, Elsevier, vol. 236(1).

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