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Self‐Weighted Lad‐Based Inference for Heavy‐Tailed Continuous Threshold Autoregressive Models

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  • Yaxing Yang
  • Dong Li

Abstract

This note investigates the self‐weighted least absolute deviation estimation (SLADE) of a heavy‐tailed continuous threshold autoregressive (TAR) model. It is shown that the SLADE is strongly consistent and asymptotically normal. The SLADE is global in the sense that the convergence rate is first obtained before deriving its limiting distribution. Moreover, a test for the continuity of TAR model is considered. A sign‐based portmanteau test is developed for diagnostic checking. An empirical example is given to illustrate the usefulness of our method. Combined with the results (Yang and Ling, 2017), a complete asymptotic theory on the SLADE of a heavy‐tailed TAR model is established. This enriches asymptotic theory of statistical inference in threshold models.

Suggested Citation

  • Yaxing Yang & Dong Li, 2020. "Self‐Weighted Lad‐Based Inference for Heavy‐Tailed Continuous Threshold Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(1), pages 163-172, January.
    • Handle: RePEc:bla:jtsera:v:41:y:2020:i:1:p:163-172
    DOI: 10.1111/jtsa.12492
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