An exact multivariate model-based structural decomposition

Abstract

We describe a simple procedure for decomposing a vector of time series into trend, cycle, seasonal and irregular components. Contrary to common practice, we do not assume these components to be orthogonal conditional on their past. However, the state-space representation employed assures that their smoothed estimates converge to exact values, with null variances and covariances. Among ather implications, this means that the components are not revised when the sample increases. The practical application of the method is illustrated both with simulated and real data.