A Method For FittingA pRARMAX Model: An Application To Financial Data
Ferreira, Marta; Canto e Castro, L.
Proceedings of the World Congress on Engineering (WCE 2010), June 30 - July 2, 2010, London, U.K., Vol III (2010), 2022-2026
Ferreira and Canto e Castro  introduces a power max-autoregressive process, in short pARMAX, as an alternative
to heavy tailed ARMA. An extension of pARMAX was considered
in Ferreira and Canto e Castro , by including a random
component, and hence called pRARMAX, which makes the model more flexible to applications. It was then developed a
methodology settled on minimizing the Bayes risk in classification theory, but only considering standard uniform random components. We now extend this procedure to the more general Beta distribution. We illustrate the method with an application to a financial data series. In order to improve estimates of the exceedance probabilities of levels of interest, we use Bortot and Tawn  approach and derive a threshold-dependent extremal index which relates with the coefficient of tail dependence of Ledford
and Tawn  and with the pRARMAX parameter.