Consistent LM-Tests for Linearity Against Compound Smooth Transition Alternatives

Jonathan B. Hill

No 42, Econometric Society 2004 North American Summer Meetings from Econometric Society

Abstract: We 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 Teräsvirta (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

Keywords: smooth transition models; consistent tests; nonlinearity; neural networks (search for similar items in EconPapers)
JEL-codes: C12 C45 C52 (search for similar items in EconPapers)
Date: 2004-08-11
New Economics Papers: this item is included in nep-ecm and nep-ets
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