A non-linear dynamic model for multipicative seasonal-trend decomposition

A non-linear dynamic model is introduced for multiplicative seasonal time series that follows and extends the X-11 paradigm where the observed time series is a product of trend, seasonal and irregular factors. A selection of standard seasonal and trend component models used in additive dynamic time series models are adapted for the multiplicative framework and a non-linear filtering procedure is proposed. The results are illustrated and compared to X-11 and log-additive models using real data. In particular it is shown that the new procedures do not suffer from the trend bias present in log-additive models.