Estimating Simultaneous Equation Models through an Entropy-Based Incremental Variational Bayes Learning Algorithm.

The presence of unaccounted heterogeneity in simultaneous equation models (SEMs) is frequently problematic in many real-life applications. Under the usual assumption of homogeneity, the model can be seriously misspecified, and it can potentially induce an important bias in the parameter estimates. This paper focuses on SEMs in which data are heterogeneous and tend to form clustering structures in the endogenous-variable dataset. Because the identification of different clusters is not straightforward, a two-step strategy that first forms groups among the endogenous observations and then uses the standard simultaneous equation scheme is provided. Methodologically, the proposed approach is based on a variational Bayes learning algorithm and does not need to be executed for varying numbers of groups in order to identify the one that adequately fits the data. We describe the statistical theory, evaluate the performance of the suggested algorithm by using simulated data, and apply the two-step method to a macroeconomic problem.

Improving prediction of COVID-19 evolution by fusing epidemiological and mobility data.

We are witnessing the dramatic consequences of the COVID-19 pandemic which, unfortunately, go beyond the impact on the health system. Until herd immunity is achieved with vaccines, the only available mechanisms for controlling the pandemic are quarantines, perimeter closures and social distancing with the aim of reducing mobility. Governments only apply these measures for a reduced period, since they involve the closure of economic activities such as tourism, cultural activities, or nightlife. The main criterion for establishing these measures and planning socioeconomic subsidies is the evolution of infections. However, the collapse of the health system and the unpredictability of human behavior, among others, make it difficult to predict this evolution in the short to medium term. This article evaluates different models for the early prediction of the evolution of the COVID-19 pandemic to create a decision support system for policy-makers. We consider a wide branch of models including artificial neural networks such as LSTM and GRU and statistically based models such as autoregressive (AR) or ARIMA. Moreover, several consensus strategies to ensemble all models into one system are proposed to obtain better results in this uncertain environment. Finally, a multivariate model that includes mobility data provided by Google is proposed to better forecast trend changes in the 14-day CI. A real case study in Spain is evaluated, providing very accurate results for the prediction of 14-day CI in scenarios with and without trend changes, reaching 0.93 [Formula: see text], 4.16 RMSE and 1.08 MAE.