Multivariate analysis can help to focus on economic phenomena, including trend and cyclical movements. To allow for potential correlation with seasonality, the present paper studies a three component multivariate unobserved component model, focusing on the case of quarterly data and showing that economic restrictions, including common trends and common cycles, can ensure identification. Applied to seasonal aggregate gender employment in Australia, a bivariate male/female model with a common cycle is preferred to both univariate correlated component and bivariate uncorrelated component specifications. This model evidences distinct gender-based seasonal patterns with seasonality declining over time for females and increasing for males.