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Testing for structural change of AR model to threshold AR model
Author(s) -
Berkes István,
Horváth Lajos,
Ling Shiqing,
Schauer Johannes
Publication year - 2011
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/j.1467-9892.2010.00714.x
Subject(s) - mathematics , likelihood ratio test , maxima , statistics , limiting , test statistic , autoregressive model , gaussian process , convergence (economics) , asymptotic distribution , statistic , weak convergence , gaussian , distribution (mathematics) , statistical physics , statistical hypothesis testing , mathematical analysis , mechanical engineering , art , physics , quantum mechanics , estimator , performance art , engineering , economics , art history , economic growth , computer security , computer science , asset (computer security)
The purpose of this article is to develop the likelihood ratio test for the structural change of an AR model to a threshold AR model. It is shown that the log‐likelihood ratio test converges to the maxima of a two‐parameter Gaussian process in distribution. This limiting distribution is novel and we tabulate the critical values. Some simulations are carried out to examine the finite‐sample performance of this test statistic. This article also includes a weak convergence of a two‐parameter marked empirical process, which is of independent interest.