Research
The two-speed Europe in business
cycle synchronization. Empirical Economics.
Camacho, M., Caro A. and Lopez-Buenache G.

This paper evaluates the consequences of the financial and sovereign debt crises on the evolution of the business cycle synchronization across all the Euro Area members. We take advantage of the dimension reduction properties of dynamic factor models to summarize a large dataset of macroeconomic indicators for the Euro Area countries. Then, we estimate latent state variables based on Markov-switching methodologies to obtain a time-varying measure of business cycle synchronization. The combination of these two techniques allows us to describe the evolution in the degree of coincidence of the business cycle phases along time for this set of countries. Our results suggest that there was a general decline in the degree of business cycle synchronization across the Euro Area countries following the financial and the sovereign debt crises. Although they have recovered the levels of business cycle synchronization exhibited before these events, there are significant differences across countries in the required time to recover those levels.
Selecting the number of factors in multi‐variate time series. Journal of Time Series Analysis.
Caro, A. and Peña D.
How many factors are there? It is a critical question that researchers and practitioners deal with when estimating factor models. We proposed a new eigenvalue ratio criterion for the number of factors in static approximate factor models. It considers a pooled squared correlation matrix which is defined as a weighted combination of the main observed squared correlation matrices. Theoretical results are given to justify the expected good properties of the criterion, and a Monte Carlo study shows its good finite sample performance in different scenarios, depending on the idiosyncratic error structure and factor strength. We conclude comparing different criteria in a forecasting exercise with macroeconomic data.
Forecasting of economic time series with big data: perspective, advances and comparisons. FUNCAS
Caro, A. and Peña D.
This paper analyzes how economic forecasting has evolved based on the available data and how the recent availability of massive data is transforming the methods used for forecasting. Three periods in the evolution of economic and business forecasting procedures are briefly reviewed and the characteristics of a fourth stage that began in this century with the Big Data revolution are presented. The methodological changes
to build predictions based on econometric, statistical and Machine Learning models are analyzed and some of the most used for prediction with time series are described. As an illustration, we compare the predictions of a set of variables that describe the business cycle in OECD countries obtained with a dynamic factorial model and a recurrent neural network.

What drives industrial energy prices? Economic Modelling.
Camacho, M., Caro A. and Peña, D.
Understanding whether the drivers of industrial energy prices are worldwide, group-specific or country-specific is a key issue in economics. This requires flexible econometric models to examine large data sets containing a significant variety of industrial sectors in different countries. To this end, we propose an extension of a dynamic factor model with group structure to account for observable country-specific explanatory variables and develop Monte Carlo simulations to show its good finite sample performance. Using data from 12 industrial sectors in 30 countries during the period from 1995 to 2015, we find three drivers of energy prices: (i) a common factor, the main driving force, captures the worldwide dynamics; (ii) country-specific variables, mainly related to inflation and the use of renewable and waste resources; and (iii) group-specific factors, which are more related to country affiliation than to sector classification.

The waiting times distribution of Spanish public hospitals: a GAMLSS approach. Investigaciones Regionales - Journal of Regional Research.
Caro, A. and De Haro-García J.
Patients’ waiting times are caused by the imbalance between the available supply and the existing demand in the health sector. Exceeding maximum waiting times may worsen diseases and entail additional costs to public health systems. This paper studies the theoretical probability distribution that best fits the average waiting times for non-urgent surgeries and first outpatient consultations for Spanish public hospitals in the region of Andalusia. For doing this we apply Generalized Additive Models for Location, Scale and Shape, which cover a wide range of probability distributions. The final models will help health authorities to better manage resources.
