Extremes of multivariate ARMAX processes

2012/12/09 by Марта Феррейра, Ferreira, Marta, Helena Ferreira +1
Economics, Econometrics and Finance · #60G70 #FOS: Mathematics #Financial Risk and Volatility Modeling #Market Dynamics and Volatility #Monetary Policy and Economic Impact #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1212.1885

openalex publication_date 2012/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a new multivariate time series model by generalizing the ARMAX process in a multivariate way. We give conditions on stationarity and analyze local dependence and domains of attraction. As a consequence of the obtained result, we derive a new method of construction of multivariate extreme value copulas. We characterize the extremal dependence by computing the multivariate extremal index and bivariate upper tail dependence coefficients. An estimation procedure for the multivariate extremal index shall be presented. We also address the marginal estimation and propose a new estimator for the ARMAX autoregressive parameter.

Citations

• Statistics for near independence in multivariate extreme values
• Construction of asymmetric multivariate copulas

Related

• Extremal behavior of pMAX processes
• Multivariate maxima of moving multivariate maxima
• Extremes of scale mixtures of multivariate time series
• Generating multivariate extreme value distributions
• Statistical models for dynamics in extreme value processes