This paper investigates the all important issue of diagnostic tests, including unit roots and cointegration, in the tourism demand modelling literature. The origins of this study lie in the apparent lack in the tourism economics literature of detail concerning the diagnostic test aspect. Study of this deficiency has suggested that previous literature on tourism demand modelling may be divided into two categories: the pre-1995 and post-1995 studies. It was found that the pre-1995 and some post-1995 studies have ignored unit root tests and co-integration and, hence, are vulnerable to the so-called spurious regression problem. In highlighting the key diagnostic tests reported by post-1995 studies, this paper contends that there is no need to report the autoregressive conditional heteroskedasticity (ARCH) test, which is applicable only to financial market analysis where the dependent variable is return on an asset. More generally, heteroskedasticity is not seen as a problem in time-series data. However, the reporting of a greater than necessary range of diagnostic tests - some of which do not have any theoretical justification with regard to tourism demand analysis - does not diminish the precision of the results or the model. This paper should appeal to scholars involved in tourism demand modelling.