Information, Data Dimension, and Factor Structure

This paper employs concepts from information to choosing the dimension of a data set. We calculate relative measures of information in the data in terms of eigenvalues and derive criteria to determine the ‘optimal’ size of the data set, in particular whether an extra variable adds information. The methods can be used as a first step in the construction of a dynamic factor model or a leading index, as illustrated with a macroeconomic data set on The Netherlands