Testing additive assumptions on means of regular monitoring data: a multivariate nonstationary time series approach

Abstract

In the analysis of surface meteorological data, observations are usually recorded regularly and frequently in time at multiple but fixed locations in space. The data can thus be viewed as multivariate time series in which a small number of lengthy time series is observed. Motivated by a temperature data, the current paper considers the problem of testing the additive assumption of location and time effects via a multivariate time series approach. Test statistics based on both maximum absolute and integrated squared deviations are proposed and their asymptotic properties are studied for a general class of multivariate nonstationary processes. The results are illustrated in a simulation study and applied to temperature data.