2007/07/26 by Bojan Basrak, Johan Segers, Basrak, Bojan +1 · 6 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #60F05 (Primary) #60G70 (Secondary) #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.0707.3989
openalex publication_date 2007/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A multivariate, stationary time series is said to be jointly regularly varying if all its finite-dimensional distributions are multivariate regularly varying. This property is shown to be equivalent to weak convergence of the conditional distribution of the rescaled series given that, at a fixed time instant, its distance to the origin exceeds a threshold tending to infinity. The limit object, called the tail process, admits a decomposition in independent radial and angular components. Under an appropriate mixing condition, this tail process allows for a concise and explicit description of the limit of a sequence of point processes recording both the times and the positions of the time series when it is far away from the origin. The theory is applied to multivariate moving averages of finite order with random coefficient matrices.