Max Autoregressive Processes: Approximations and Time Series Models with Log-Positive Alpha Stable Noises and Hidden Max Gumbel Shocks

• Activity Number: 352
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Bin Zhu*+ and Zhengjun Zhang and Philippe Naveau
• Companies: University of Wisconsin at Madison and University of Wisconsin and Laboratoire des Sciences du Climat et de l'Environnement
• Keywords: Extreme Value Theory ; Dependence ; Gumbel Distribution ; Autoregressive Model

Abstract

Max-autoregressive (MAR) processes and moving maxima (MM) processes are naturally adapted from linear autoregressive (AR) processes and moving average (MA) processes in modeling clustered maxima in time series. Yet, applications of MAR processes and MM processes are still sparse due to some di±culties of statistical parameter estimation and some abnormality of the processes, basically that ratios of observations can take constant values. The objective of this present work is to introduce a new model that is closely related to MAR processes and is free of the aforementioned abnormality. A logarithm transformation of the new model leads to time series models with log-positive alpha stable noises and hidden max Gumbel shocks. Theoretical properties of new models are derived.