An extended sparsemax-linearmoving model with application to high-frequency financial data

There continues to be unfading interest in developing parametric max-stable processes for modelling tail dependencies and clustered extremes in time series data.However,this comes with some difficulties mainly due to the lack of models that fit data directly without transforming the data and the barriers in estimating a significant number of parameters in the existing models.In thiswork,we study the use of the sparsemaxima ofmovingmaxima(M3)process.After introducing random effects and hidden Fréchet type shocks into the process,we get an extended maxlinear model.The extended model then enables us to model cases of tail dependence or independence depending on parameter values.We present some unique properties including mirroring the dependence structure in real data,dealing with the undesirable signature patterns found in most parametricmax-stable processes,and being directly applicable to real data.ABayesian inference approach is developed for the proposed model,and it is applied to simulated and real data.