Nowadays, procedures for testing the null hypothesis of linearity of a (univariate or multivariate) stochastic process are well known, almost all of them based on the assumption that their paths (i.e. observed time series) are complete. This paper describes an approach for testing this null hypothesis in the presence of missing data, using an extension of one of the test statistics used in the literature. The alternative hypothesis is that the univariate stochastic process of interest follows a threshold autoregressive (TAR) model. It is found that if the missing-data percentage is low, the null distribution of the proposed test statistic is maintained; while if it is high, it is not. A threshold value for the missing-data percentage is detected, which can be utilized in practice.