Discovering Specific Common Trends in a Large Set of Disaggregates: Statistical Procedures, their Properties and an Empirical Application*

Abstract

Macroeconomic variables are weighted averages of a large number of components. Our objective is to model and forecast all of the N components of a macro variable. The main feature of our proposal consists of discovering subsets of components that share single common trends while neither assuming pervasiveness nor imposing special restrictions on the serial or cross‐sectional idiosyncratic correlation. We adopt a pairwise approach and study its statistical properties. Our asymptotic theory works both with fixed N and T→∞ and with [T,N]→∞. We show that the pairwise approach can be implemented using three alternative strategies, which take into account alternative characteristics of the data generating process. The paper includes an application to the US CPI broken down into 159 components.

Forecasting Real GDP Growth for Africa

“…In a sense, our approach bears similarities with a recent pairwise-based approach to model a macroeconomic variable that is the weighted average of many components, see Carlomagno and Espasa (2021).…”