In recent years, analysis of financial time series focuses largely on data related to market trading activity. Apart from modeling of the conditional variance of returns within the generalized autoregressive conditional heteroskedasticity (GARCH) family of models, presently attention is also devoted to that of other market variables, for instance volumes, number of trades or financial durations. To this end, a large group of researchers focus their studies on a class of model that is referred to in the literature as the multiplicative error model (MEM), which is considered particularly for modeling non-negative time series processes. The goal of the current paper is to establish an alternative misspecification test for the MEM of non-negative time series processes. In the literature, although several procedures are available to perform hypothesis testing for the MEM, the newly proposed testing procedure is particularly useful in the context of the MEM of waiting times between financial events since its outcomes have a number of important implications on the fundamental concept of point processes. Finally, the current paper makes a number of statistical contributions, especially in making a head way into nonparametric hypothesis testing of unobservable variables.