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Conditions are obtained for a Gaussian vector autoregressive time series of order k, VAR(k), to have univariate margins that are autoregressive of order k or lower‐dimensional margins that are also VAR(k). This can lead to d‐dimensional VAR(k) models that are closed with respect to a given partition {S1,...,Sn} of {1,...,d} by specifying marginal serial dependence and some cross‐sectional dependence parameters. The special closure property allows one to fit the subprocesses of multi‐variate time series before assembling them by fitting the dependence structure between the subprocesses. We revisit the use of the Gaussian copula of the stationary joint distribution of observations in the VAR(k) process with non‐Gaussian univariate margins but under the constraint of closure under margins. This construction allows more flexibility in handling higher‐dimensional time series and a multi‐stage estimation procedure can be used. The proposed class of models is applied to a macro‐economic data set and compared with the relevant benchmark models. [ABSTRACT FROM AUTHOR]

The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously large. Various alternative dependence measures and representations have been proposed, with the most well-known being hidden regular variation and the conditional extreme value model. These varying depictions of extremal dependence arise through consideration of different parts of the multivariate domain, and particularly through exploring what happens when extremes of one variable may grow at different rates from other variables. Thus far, these alternative representations have come from distinct sources, and links between them are limited. In this work we elucidate many of the relevant connections through a geometrical approach. In particular, the shape of the limit set of scaled sample clouds in light-tailed margins is shown to provide a description of several different extremal dependence representations. [ABSTRACT FROM AUTHOR]

The global financial crisis of 2007–2009 revealed the great extent to which systemic risk can jeopardize the stability of the entire financial system. An effective methodology to quantify systemic risk is at the heart of the process of identifying the so-called systemically important financial institutions for regulatory purposes as well as to investigate key drivers of systemic contagion. The article proposes a method for dynamic forecasting of CoVaR, a popular measure of systemic risk. As a first step, we develop a semi-parametric framework using asymptotic results in the spirit of extreme value theory (EVT) to model the conditional probability distribution of a bivariate random vector given that one of the components takes on a large value, taking into account important features of financial data such as asymmetry and heavy tails. In the second step, we embed the proposed EVT method into a dynamic framework via a bivariate GARCH process. An empirical analysis is conducted to demonstrate and compare the performance of the proposed methodology relative to a very flexible fully parametric alternative. [ABSTRACT FROM AUTHOR]

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Debris flows carry a tremendous potential for physical destruction as well as a threat to human lives. Quantitative analysis of their frequency and magnitude relation is key to the development of mitigation measures to reduce hazard and risk. Yet, the data available for such analysis are typically very sparse, leading to point estimates for return levels that are too imprecise to be of practical value. The aim of the paper is to demonstrate how additional sources of information, in particular, expert judgment which uses physical causes and the size of the active area producing loose sediments, can be incorporated to produce more precise estimates with a smaller upper endpoint of interval estimates of extreme return levels. A Bayesian framework for extreme value analysis is used. We provide a rationale for the prior choice and discuss how its parameters can be elicited from the expert's knowledge. A case study of debris flows at Capricorn Creek in Western Canada is used to illustrate our methodology. [ABSTRACT FROM AUTHOR]