Search

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]

Abstract: The residual dependence coefficient was originally introduced by Ledford and Tawn (1996) [25] as a measure of residual dependence between extreme values in the presence of asymptotic independence. We present a geometric interpretation of this coefficient with the additional assumptions that the random samples from a given distribution can be scaled to converge onto a limit set and that the marginal distributions have Weibull-type tails. This result leads to simple and intuitive computations of the residual dependence coefficient for a variety of distributions. [Copyright &y& Elsevier]

Consider a multivariate distribution of (X , Y) , where X is a vector of predictor variables and Y is a response variable. Results are obtained for comparing the conditional and marginal tail indices, ξ Y | X (x) and ξ Y , based on conditional distributions { F Y | X (⋅ | x) } and marginal distribution F Y , respectively. For a multivariate distribution based on a copula, the conditional tail index can be decomposed into a product of copula-based conditional tail indices and the marginal tail index. In some applications, one may want ξ Y | X (x) to be non-constant, and some new copula families are derived to facilitate this. [ABSTRACT FROM AUTHOR]

Extremely rapid, flow-like landslides pose a significant hazard worldwide; however, the analysis of the impact area and velocity of these flows is not routine. Semi-empirical numerical models are one tool that is available for performing this sort of analysis. These models are physically based; however, certain input parameters are determined through model calibration, using back-analysis of real landslide cases. Objective, repeatable calibration methods are needed for this approach to be useful for landslide runout prediction. The present analysis describes the application of optimization theory and Bayesian statistics to calibrate these types of models. Two complementary methods are presented. The first uses the Gauss-Marquardt-Levenberg optimization algorithm to efficiently determine a set of best-fit calibrated model parameters. The second uses a posterior analysis to quantify errors associated with parameter calibration, which can then be used for probabilistic forward analysis. Three case histories are presented to demonstrate how the new methods are able to rapidly calibrate a runout model, reduce subjectivity inherent in the calibration process, and provide information on parameter uncertainty. [ABSTRACT FROM AUTHOR]

Rock avalanches can be a significant hazard to communities located in mountainous areas. Probabilistic predictions of the 3D impact area of these events are crucial for assessing rock avalanche risk. Semi-empirical, calibration-based numerical runout models are one tool that can be used to make these predictions. When doing so, uncertainties resulting from both noisy calibration data and uncertain governing movement mechanism(s) must be accounted for. In this paper, a back-analysis of a database of 31 rock avalanche case histories is used to assess both of these sources of uncertainty. It is found that forecasting results are dominated by uncertainties associated with the bulk basal resistance of the path material. A method to account for both calibration and mechanistic uncertainty is provided, and this method is evaluated using pseudo-forecasts of two case histories. These pseudo-forecasts show that inclusion of expert judgement when assessing the bulk basal resistance along the path can reduce mechanistic uncertainty and result in more precise predictions of rock avalanche runout. [ABSTRACT FROM AUTHOR]