Dynamic specification tests for dynamic factor models

We derive computationally simple expressions for score tests of misspecification in para- metric dynamic factor models using frequency domain techniques. We interpret those diag- nostics as time domain moment tests which assess whether certain autocovariances of the smoothed latent variables match their theoretical values under the null of correct model speci…cation. We also reinterpret reduced-form residual tests as checking specific restric- tions on structural parameters. Our Gaussian tests are robust to nonnormal, independent innovations. Monte Carlo exercises con…rm the …nite sample reliability and power of our proposals. Finally, we illustrate their empirical usefulness in an application that constructs a US coincident indicator..