An extended sparse max-linear moving 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 this work, we study the use of the sparse maxima of moving maxima (M3) process. After introducing random effects and hidden Fréchet type shocks into the process, we get an extended max-linear 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 parametric max-stable processes, and being directly applicable to real data. A Bayesian inference approach is developed for the proposed model, and it is applied to simulated and real data.