Dynamic Specification Tests for Static Factor Models

We derive computationally simple score tests of serial correlation in the levels and squares of common and idiosyncratic factors in static factor models. The implicit orthogonality conditions resemble the orthogonality conditions of models with observed factors but the weighting matrices refl ect their unobservability. We derive more powerful tests for elliptically symmetric distributions, which can be either parametrically or semipametrically specified, and robustify the Gaussian tests against general non-normality. Our Monte Carlo exercises assess the finite sample reliability and power of our proposed tests, and compare them to other existing procedures. Finally, we apply our methods to monthly US stock returns.