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Many macroeconomic time series are characterised by nonlinearity both in theconditional mean and in the conditional variance and, in practice, it isimportant to investigate separately these two aspects. Here we address theissue of testing for threshold nonlinearity in the conditional mean, in thepresence of conditional heteroskedasticity. We propose a supremum LagrangeMultiplier approach to test a linear ARMA-GARCH model against the alternativeof a TARMA-GARCH model. We derive the asymptotic null distribution of the teststatistic and this requires novel results since the difficulties of workingwith nuisance parameters, absent under the null hypothesis, are amplified bythe non-linear moving average, combined with GARCH-type innovations. We showthat tests that do not account for heteroskedasticity fail to achieve thecorrect size even for large sample sizes. Moreover, we show that the TARMAspecification naturally accounts for the ubiquitous presence of measurementerror that affects macroeconomic data. We apply the results to analyse the timeseries of Italian strikes and we show that the TARMA-GARCH specification isconsistent with the relevant macroeconomic theory while capturing the mainfeatures of the Italian strikes dynamics, such as asymmetric cycles andregime-switching.

Testing for Threshold Effects in Presence of Heteroskedasticity and Measurement Error with an application to Italian Strikes