Time series with season-dependent autocorrelation structure are commonly modelled using periodic autoregressive moving average (PARMA) processes. In most applications, the moving average terms are excluded for ease of estimation. We propose a new class of periodic unobserved component models (PUCM). Parameter estimates for PUCM are readily interpreted; the estimated coefficients correspond to variances of the measurement noise and of the error terms in unobserved components. We show that PUCM have correlation structure equivalent to that of a periodic integrated moving average (PIMA) process. Results from practical applications indicate that our models provide a natural framework for series with periodic autocorrelation structure both in terms of interpretability and forecasting accuracy. Copyright © 2008 John Wiley & Sons, Ltd.