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We propose a general framework for Maximum Likelihood (ML) and Bayesian estimation of income distributions based on grouped data information. The asymptotic properties of the ML estimators are derived and Bayesian parameter estimates are obtained by Monte Carlo Markov Chain (MCMC) techniques. A comprehensive simulation experiment shows that obtained estimates of the income distribution are very precise and that the proposed estimation framework improves the statistical precision of parameter estimates relative to the classical multinomial likelihood. The estimation approach is finally applied to a set of countries included in the World Bank database PovcalNet.

We propose a copula-based periodic mixed frequency generalized autoregressive (GAS) framework in order to model and forecast the intraday exposure conditional value at risk (ECoVaR) for an intraday asset return and the corresponding market return. In particular, we analyze GAS models that account for long-memory-type of dependencies, periodicities, asymmetric nonlinear dependence structures, fat-tailed conditional return distributions, and intraday jump processes for asset returns. We apply our framework in order to analyze the ECo-VaR forecasting performance for a large data set of intraday asset returns of the S&P500 index.

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