Methodology (stat.ME)

Abstract: Systemic risk measures have been shown to be predictive of financial crises and declines in real activity. Thus, forecasting them is of major importance in finance and economics. In this paper, we propose a new forecasting method for systemic risk as measured by the marginal expected shortfall (MES). It is based on first de-volatilizing the observations and, then, calculating systemic risk for the residuals using an estimator based on extreme value theory. We show the validity of the method by establishing the asymptotic normality of the MES forecasts. The good finite-sample coverage of the implied MES forecast intervals is confirmed in simulations. An empirical application to major US banks illustrates the significant time variation in the precision of MES forecasts, and explores the implications of this fact from a regulatory perspective.

Abstract: The Whittle-Mat\'ern fields are a recently introduced class of Gaussian processes on metric graphs, which are specified as solutions to a fractional-order stochastic differential equation on the metric graph. Contrary to earlier covariance-based approaches for specifying Gaussian fields on metric graphs, the Whittle-Mat\'ern fields are well-defined for any compact metric graph and can provide Gaussian processes with differentiable sample paths given that the fractional exponent is large enough. We derive the main statistical properties of the model class. In particular, consistency and asymptotic normality of maximum likelihood estimators of model parameters as well as necessary and sufficient conditions for asymptotic optimality properties of linear prediction based on the model with misspecified parameters. The covariance function of the Whittle-Mat\'ern fields is in general not available in closed form, which means that they have been difficult to use for statistical inference. However, we show that for certain values of the fractional exponent, when the fields have Markov properties, likelihood-based inference and spatial prediction can be performed exactly and computationally efficiently. This facilitates using the Whittle-Mat\'ern fields in statistical applications involving big datasets without the need for any approximations. The methods are illustrated via an application to modeling of traffic data, where the ability to allow for differentiable processes greatly improves the model fit.