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

Yaxing Yang and Shiqing Ling

Journal of Business & Economic Statistics, 2017, vol. 35, issue 2, 318-333

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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:taf:jnlbes:v:35:y:2017:i:2:p:318-333

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DOI: 10.1080/07350015.2015.1064433

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