Integer-valued max-autoregressive models

The talk addresses an introduction to integer-valued max-autoregressive models. The parameter estimation for such models, e.g., the max-INAR(1) model, seems to be straightforward. The max-INAR(1) model is a Markov chain and maximum likelihood estimation with numerical optimization routines seems to be easily applicable. But if the observed counts attain very large values, numerical issues frustrate this plan. The structure of the max-INAR(1) process will be used to show up a way to circumvent this problem. An example of the parameter estimation procedure with real data (counts of cinema visitors) demonstrates the application.