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Self‐Weighted Lad‐Based Inference for Heavy‐Tailed Continuous Threshold Autoregressive Models
Author(s) -
Yang Yaxing,
Li Dong
Publication year - 2020
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12492
Subject(s) - mathematics , autoregressive model , asymptotic distribution , inference , least absolute deviations , sign (mathematics) , convergence (economics) , autoregressive–moving average model , tar (computing) , asymptotic analysis , statistical inference , statistics , econometrics , estimator , mathematical analysis , artificial intelligence , computer science , economics , programming language , economic growth
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.