A complete convergence theorem for stationary regularly varying multivariate time series

For a class of stationary regularly varying and weakly dependent multivariate time series (X _n ), we prove the so-called complete convergence result for the space–time point processes of the form \(N_{n} = \sum _{i=1}^{n} \delta _{(i/n, \boldsymbol {X}_{i}/a_{n})}.\) As an application of our main theorem, we give a simple proof of the invariance principle for the corresponding partial maximum process.