Selecting the number of factors in multi‐variate time series

Abstract

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.