Evaluating restricted Common Factor models for non-stationary data

Approximate factor models with restrictions on the loadings may be interesting both for structural analysis (simpler structures are easier to interpret) and forecasting (parsimonious models typically deliver superior forecasting performances). However, the issue is largely unexplored. In particular, no currently available test is entirely suitable for the empirically important case of non-stationary data. Building on the intuition that de-factoring the data under a correct set of restrictions will lower the number of factors, a bootstrap test based on the comparison of the number of factors selected for the raw and de-factored data is proposed. The test is shown analytically to be asymptotically valid and by simulation to have good small sample properties.