Common factors for seasonal multivariate time series are usually obtained by first filtering the series to eliminate the seasonal component and then extracting the nonseasonal common factors. This approach has two drawbacks. First, we cannot detect common factors with seasonal structure; second, it is well known that a deseasonalized time series may exhibit spurious cycles that the original data do not contain, which can make more difficult the detection of ∗Corresponding author: fhnietos@unal.edu.co Phone (+57) 1-3165000