Two simple tests of the trend hypothesis under time-varying variance

•This paper investigates the effects of time-varying variance on two recent linear trend tests.•We find time-varying variance results in obviously different null distributions.•We propose two new linear trend tests which are robust to time-varying variance.•Monte Carlo simulations and an empirical application are provided.

This paper investigates the effects of time-varying variance on the linear trend tests proposed by Harvey et al. (2007) (HLT) and Perron and Yabu (2009) (PY) and finds time-varying variance results in obviously different null distributions. We propose two new robust linear trend tests. An empirical application highlights the usefulness of our tests.