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Stationarity testing under nonlinear models. Some asymptotic results
Author(s) -
Landajo Manuel,
Presno María José
Publication year - 2010
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.1467-9892.2010.00672.x
Subject(s) - mathematics , asymptotic distribution , lagrange multiplier , consistency (knowledge bases) , nonlinear system , series (stratigraphy) , score test , null hypothesis , limiting , statistical hypothesis testing , asymptotic analysis , mathematical optimization , econometrics , statistics , mechanical engineering , paleontology , geometry , quantum mechanics , estimator , engineering , biology , physics
Stationarity testing for nonlinear time series models which include several smooth trend components with (possibly) unknown parameters is considered. A pseudo‐Lagrange multiplier stationarity test is proposed and its asymptotic behaviour is derived. The limiting null distribution generally depends on the unknown parameters of the model. A bootstrap approach permits this problem to be circumvented and consistency of the bootstrapped test is obtained. The theoretical analysis is complemented with a simulation study which allows us to check the performance of the test in finite samples. The article ends with an empirical application.