Estimation of the Parameter of a pARMAX Model


  • Marta Ferreira University of Minho



extreme value theory, max-autoregressive processes


Max-autoregressive models for time series data are useful when we want to make inference about rare events, mainly in areas like hydrology, geophysics and finance. In fact, they are more convenient for analysis than heavy-tailed ARMA, as their finite-dimensional distributions can easily be written explicitly. The recent power max-autoregressive model (pARMAX) has the interesting feature of describing an asymptotic independent tail behavior, a property that can be observed in various data series. An estimator of the model parameter c (0 < c < 1) is already available in the literature, but only in the restrictive case c > 1/2. Here it is presented an estimator for all c ∈ (0, 1). Consistency and asymptotic normality are also stated.



How to Cite

Ferreira , M. (2010). Estimation of the Parameter of a pARMAX Model. REVSTAT-Statistical Journal, 8(2), 139–149.