Heavy tailed time series with extremal independence

Abstract

International audienceWe consider strictly stationary heavy tailed time series whose finite-dimensional exponent measures are concentrated on axes, and hence their extremal properties cannot be tackled using classical multivariate regular variation that is suitable for time series with extremal dependence. We recover relevant information about limiting behavior of time series with extremal independence by introducing a sequence of scaling functions and conditional scaling exponent. Both quantities provide more information about joint extremes than a widely used tail dependence coefficient. We calculate the scaling functions and the scaling exponent for variety of models, including Markov chains, exponential autoregressive model, stochastic volatility with heavy tailed innovations or volatility

Extremes of randomly scaled Gumbel risks

“…We refer to, e.g., [1,2,4,10,11,15,[26][27][28] for related results concerned with the asymptotic tail behaviour of the products of rvs.…”

“…The study of products of rvs is of interest for numerous applications, see e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13]. We mention below three with Y 1 > 0 being independent of Y 2 .…”

kth-order Markov extremal models for assessing heatwave risks

“…Kulik and Soulier (2015) and Papastathopoulos et al (2017) consider tail chains for first-order asymptotically independent processes. Normalising using a subtraction of u leads to degeneracy in this case, and less powerful location-scale norming is required.…”

Estimation of the marginal expected shortfall under asymptotic independence

“…Apart from the continuity, we do not impose any condition on the marginal distribution of Y . Kulik and Soulier () have provided the asymptotic property of MES for regularly varying time series { X h } with extremal independence (meaning that X 0 and X h are asymptotically independent for h >0), using conditional extreme value approach, which is an alternative way to model asymptotic independence, introduced in Heffernan and Resnick () and Heffernan and Tawn (). No estimators are yet proposed.…”