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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]

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]