A generalization of conventional mean regression models is obtained by introducing additional regression equations for higher moments of the conditional distribution of the response variable. In this paper, it is shown how artificial neural networks can be used to construct corresponding efficiently parameterized distributional regression models based on the fact that all conditional moments depend on the same set of explanatory variables. In particular, the focus is on explicitly maximizing a suitable likelihood function subject to the neural network parameters. The size of the network is kept in a reasonable balance to the number of available observations, allowing for inference in terms of the calculation of (approximate) confidence and prediction intervals, most importantly for the marginal effects of the considered explanatory variables on the moment parameters. This contributes significantly to the (stochastic) interpretability of the model. The practical usefulness is demonstrated by analyzing several real-world data sets and comparing the proposed framework to existing distributional regression frameworks.

The framework of (RES 2005) allows quantifying the asymmetry of unknown loss functions based on observed forecasts as well as for rationality testing under asymmetric loss. To this end, they formalized a class of loss functions characterized by the asymmetry and the tail weight parameter, which nest asymmetric linear and asymmetric quadratic loss functions. Given the shape of these loss functions, they derive tractable moment conditions for optimality of forecasts. In particular, the "generalized" forecast error should have zero conditional expectation given all predictors available. Based on these moments, GMM estimation of the asymmetry parameter is possible. Under conditions, GMM is consistent and asymptotically normal. Formulas for standard errors allow to conduct inference, typically about the asymmetry parameter.

However, forecast errors are likely to be noisy (e.g. from estimating the forecast models), such that Elliott et al.'s assumptions are only approximately met. We follow West (1996) in modelling the estimation noise and assess, theoretically and in simulations, the impact of such noise on the estimators of loss function parameters. We show that consistency of GMM of loss function parameters is typically not affected, but Elliott et al.'s standard errors underestimate the true variability of the estimators. Like in West's analysis of the Diebold-Mariano test, the correct standard errors depend on the forecast model and on the estimation scheme.

While one often observes forecasts, information on how the forecasts were generated is seldom available, such that adjusting standard errors is not often feasible. Notwithstanding, our second contribution is to propose a conditional moment test for the parameters of the loss function that is robust to estimation noise, and find it to have good size. Size control implies somewhat reduced power. Yet, the test has the further advantage of being able to identify subsamples where the null is violated.

Moving-block bootstrap procedures have become a preferred method to determine the sampling uncertainty of vector autoregressive (VAR) model estimation, most prominently visualized as confidence bands around impulse response functions (IRF). In this study, we extend these inferential methods for multivariate time series by the cross-section dimension and compile recursive-design moving-block bootstrap procedures for proxy-identified panel VAR models and their structural IRF. The procedures resample blocks of estimated error terms either in (i) the temporal, (ii) the cross-sectional, or (iii) both dimensions jointly. Their asymptotic assessment and a finite-sample Monte-Carlo study both suggest the preferred use of panel-block resampling in both dimensions when confronted with data properties typically found in empirical panel VAR applications.

pvars offers a seamless implementation of vector autoregressive (VAR) methods for heterogeneous panel data. The R-package comprises panel cointegration rank tests which can account for cross-sectional dependence and for structural breaks in the deterministic term. The implemented panel SVAR models can be estimated under these specifications with pooled cointegrating vectors and identified by various panel identification procedures. In this article, we review these methods and present their

modular implementation in R. Two empirical illustrations reproduce examples from the literature step-by-step and guide the pvars user into conducting own analyses.