Distinguishing Time-varying Factor Models

Time-varying factor models have been widely used to model changing relationships among economic and financial variables. The existing literature usually specifies the time-varying factor loadings as deterministic functions of time or unit root processes. This paper proposes two consistent tests to distinguish these two specifications based on a randomization approach. By setting the null hypothesis as either specification, we show that the proposed test statistics follow an asymptotic chi-squared distribution under the respective null hypotheses and diverge to infinity in probability under the respective alternatives. Simulation studies reveal that both test statistics perform reasonably well in finite samples. We apply the proposed tests to the U.S. macroeconomic and global macroeconomic and financial datasets. The results suggest that the time-varying factor loadings as deterministic functions of time should be adopted for these two applications.