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 reflect their unobservability. Our tests are targeted to elliptically symmetric distributions,
which can be either parametrically or semipametrically specified, but we also 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.