Both static and dynamic factor models are incredibly popular in economics, finance and other disciplines that analyze large data sets covering time series observations on multiple variables because they allow a few latent factors explain their shared dynamics and covariations. These models estimate unobserved factors and their joint dynamics, and have wide-ranging applications in areas such as forecasting, time series interpolation, macroeconomic monitoring and asset pricing. Factor models can be estimated using tools such as the Kalman Filter and various solution algorithms, with the Expectation Maximization (EM) algorithm being widely used in the economics literature. However, these estimation methods often rely heavily on the assumption of joint normality of the latent factors and the observed variables. If the distribution or other aspects of the factor model are misspecified, then Gaussian estimation is often difficult to interpret. Unfortunately, it is not easy to detect misspecification given that the factors are typically unobservable. The aim of this project, which will be the first chapter of my dissertation, is to provide a simple to compute and especially interpret diagnostic that would allow empirical to assess the correct specification of the static or dynamic factor models that they estimate.

The contributions of this project are fourfold. First, I will derive an explicit expression for the information matrix test for Gaussian factor models whether the factors are observed or remain latent. Second, I will provide an intuitive interpretation of the influence functions underlying the information matrix test. Third, I will show that the information matrix test is easy to implement and, through simulation procedures, illustrate that it is effective in detecting deviations from correct specification. Finally, I will apply the test to an empirically relevant real-world situation using a coincident business cycle index as an example that illustrates its practical usefulness. This application builds on the work of Camacho et al. (2015), who found that the coincident index from one sided Kalman filter is not always synchronized with the expansions and recessions defined by the US NBER. Specifically, I will model the U.S. business cycle using four coincident economic indicators—industrial production, wage income, unemployment, and real manufacturing and trade sales using a dynamic factor model. Then, after estimating the model parameters by maximum likelihood, I will apply my test to detect possible misspecifications.