Consistent LM-Tests for Linearity Against Compound Smooth Transition Alternatives
AbstractWe develop LM-tests of linearity that are consistent against a class of Compound Smooth Transition Autoregressive (CoSTAR) models of the conditional mean. Our method is an extension of the sup-test developed by Bierens (1990) and Bierens and Plobeger (1997), provides maximal power against popular STAR alternatives and is consistent against any deviation from the null hypothesis. Moreover, the test method can be extended to consistent tests of number of threshold regimes, flexible parametric forms, conditional homoscedasticity against linear or smooth transition GARCH, and causality tests of out-of-sample predictive accuracy. Of particular note, we improve on Bierens's (1990) test theory by considering vector conditional moments which lead to an LM sup-test statistic that is never degenerate under the alternative of functional mis-specification. Moreover, our test is a true test against smooth transition alternatives, whereas the universally employed polynomial regression test of TerÃ¤svirta (1994) requires the assumption that the true data generating mechanism is STAR. A simulation study demonstrates that the suggested STAR sup-statistic renders a test with superlative empirical size and power attributes, in particular in comparison to the Bierens (1990) test, the neural test by Lee, White and Granger (1993), and specifically the polynomial regression test employed throughout the STAR literature. Finally, we apply the new tests to various macroeconomic processes
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Bibliographic InfoPaper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 42.
Date of creation: 11 Aug 2004
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smooth transition models; consistent tests; nonlinearity; neural networks;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-10-30 (All new papers)
- NEP-ECM-2004-10-30 (Econometrics)
- NEP-ETS-2004-10-30 (Econometric Time Series)
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