Time Series Factor Analysis with an Application to Measuring Money

Time series factor analysis (TSFA) and its associated statistical theory is developed. Unlike dynamic factor analysis (DFA), TSFA obviates the need for explicitly modeling the process dynamics of the underlying phenomena. It also differs from standard factor analysis (FA) in important respects: the factor model has a nontrivial mean structure, the observations are allowed to be dependent over time, and the data does not need to be covariance stationary as long as differenced data satisfies a weak boundedness condition. The effects on the estimation of parameters and prediction of the factors is discussed. The statistical properties of the factor score predictor are studied in a simulation study, both over repeated samples and within a given sample. Some apparent anomalies are found in simulation experiments and explained analytically.