Abstract
In this note we study the behaviour of an asymptotic test for linearity against the threshold autoregressive moving average model in presence of conditional heteroskedasticity. We recall the relevant asymptotic theory both under the null and the alternative hypotheses for a supremum Lagrange Multiplier test statistic in presence of i.i.d. errors. By means of a small simulation study we show that when the innovations follow a GARCH process the size of the test can be severely biased and we discuss possible solutions to the problem.