Long-term phenotypic stasis is frequently observed in the fossil record, but not readily predicted from microevolutionary theory. To test competing explanations for stasis on macroevolutionary time scales we need reliably estimated parameters from appropriate evolutionary models that adequately describe the evolutionary trait dynamics. Here, we develop tests to assess the adequacy of the most commonly used stasis model in evolutionary biology and apply them to time series of phenotypic traits from fossil lineages. Of the 572 fossil time series we analyzed from the literature, 263 times series showed a better fit to the stasis model relative to alternative models, but only 172 of those fitted the stasis model both in relative and absolute terms. The estimated trait variances from these 172 time series do not correlate with rough proxies of effective population size. Our preliminary investigation of the fixed-optimum hypothesis hence fails to give empirical support to the idea that genetic drift around a constant trait optimum is an explanation for stasis in the fossil record. We argue that optima following stationary processes on the adaptive landscape is a viable hypothesis for stasis that needs further investigation. We end by discussing how investigations of model adequacy can be a valuable approach for increasing our understanding of the dynamics of the adaptive landscape on macroevolutionary time scales.